{"id":27470,"date":"2021-02-12T13:00:41","date_gmt":"2021-02-12T13:00:41","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=27470"},"modified":"2024-07-09T05:01:08","modified_gmt":"2024-07-09T05:01:08","slug":"%e0%a4%95%e0%a5%8d%e0%a4%b2%e0%a4%be%e0%a4%b8%e0%a4%bf%e0%a4%95%e0%a4%b2-%e0%a4%b2%e0%a5%89%e0%a4%9c%e0%a4%bf%e0%a4%95-%e0%a4%a4%e0%a4%95%e0%a4%a8%e0%a5%80%e0%a4%95%e0%a5%8b%e0%a4%82-%e0%a4%95","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%95%e0%a5%8d%e0%a4%b2%e0%a4%be%e0%a4%b8%e0%a4%bf%e0%a4%95%e0%a4%b2-%e0%a4%b2%e0%a5%89%e0%a4%9c%e0%a4%bf%e0%a4%95-%e0%a4%a4%e0%a4%95%e0%a4%a8%e0%a5%80%e0%a4%95%e0%a5%8b%e0%a4%82-%e0%a4%95\/","title":{"rendered":"\u0915\u094d\u0932\u093e\u0938\u093f\u0915\u0932 \u0932\u0949\u091c\u093f\u0915 \u0924\u0915\u0928\u0940\u0915\u094b\u0902 \u0915\u093e \u092a\u094d\u0930\u0926\u0930\u094d\u0936\u0928"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>\u0915\u094d\u0932\u093e\u0938\u093f\u0915\u0932 \u0932\u0949\u091c\u093f\u0915 \u0924\u0915\u0928\u0940\u0915\u094b\u0902 \u0915\u093e \u092a\u094d\u0930\u0926\u0930\u094d\u0936\u0928<\/h1>\n<p><\/p>\n<p style=\"text-align:center;\"><strong>\u0938\u093e\u0930\u093e\u0902\u0936<\/strong><br \/><em>\u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u0938\u0902\u092f\u094b\u091c\u0928 \u0914\u0930 \u0935\u093f\u0938\u0902\u092f\u094b\u091c\u0928 \u0915\u0940 \u0936\u0941\u0930\u0942\u0906\u0924 \u0914\u0930 \u0909\u0928\u094d\u092e\u0942\u0932\u0928 \u0915\u0947 \u0932\u093f\u090f \u0915\u0908 \u0915\u094d\u0932\u093e\u0938\u093f\u0915\u0932 \u0932\u0949\u091c\u093f\u0915 \u0924\u0915\u0928\u0940\u0915\u094b\u0902 \u0915\u094b \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948, \u0938\u093e\u0925 \u0939\u0940 \u0924\u0940\u0938\u0930\u0947 \u0915\u093e \u092c\u0939\u093f\u0937\u094d\u0915\u093e\u0930 \u0914\u0930 \u0935\u093f\u0938\u094d\u092b\u094b\u091f \u0915\u0947 \u0928\u093f\u092f\u092e \u0915\u094b \u092d\u0940 \u0938\u092e\u091d\u093e\u092f\u093e \u0917\u092f\u093e \u0939\u0948, \u091c\u093f\u0938\u0947 \u0935\u093f\u0930\u094b\u0927\u093e\u092d\u093e\u0938 \u0915\u0947 \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u092d\u0940 \u091c\u093e\u0928\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0907\u0938\u0915\u0947 \u0905\u0932\u093e\u0935\u093e, \u092e\u093e\u092e\u0932\u094b\u0902 \u0926\u094d\u0935\u093e\u0930\u093e \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0914\u0930 \u0905\u092d\u093f\u0936\u093e\u092a \u0924\u0915 \u0909\u0928\u094d\u092e\u0942\u0932\u0928 \u0915\u0940 \u0924\u0915\u0928\u0940\u0915 \u0915\u094b \u092d\u0940 \u0938\u092e\u091d\u093e\u092f\u093e \u0917\u092f\u093e \u0939\u0948, \u091c\u094b \u0917\u0923\u093f\u0924\u0940\u092f \u0914\u0930 \u0924\u093e\u0930\u094d\u0915\u093f\u0915 \u092a\u094d\u0930\u0926\u0930\u094d\u0936\u0928 \u092e\u0947\u0902 \u092c\u0939\u0941\u0924 \u0909\u092a\u092f\u094b\u0917\u0940 \u0939\u0948\u0964 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0924\u0915\u0928\u0940\u0915 \u0915\u094b \u0914\u092a\u091a\u093e\u0930\u093f\u0915 \u0930\u0942\u092a \u0938\u0947 \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948 \u0914\u0930 \u0909\u0938\u0915\u0940 \u0938\u092e\u091d \u0915\u0947 \u0932\u093f\u090f \u091a\u0930\u0923-\u0926\u0930-\u091a\u0930\u0923 \u092a\u094d\u0930\u0926\u0930\u094d\u0936\u0928 \u0926\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948\u0964 \u092f\u0926\u093f \u0906\u092a \u092a\u094d\u0930\u0938\u094d\u0924\u093e\u0935\u0928\u093e\u0924\u094d\u092e\u0915 \u0924\u0930\u094d\u0915\u0936\u093e\u0938\u094d\u0924\u094d\u0930 \u092e\u0947\u0902 \u0917\u0939\u0930\u093e\u0908 \u0924\u0915 \u091c\u093e\u0928\u093e \u091a\u093e\u0939\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u0905\u092a\u0928\u0947 \u092a\u094d\u0930\u092e\u0947\u092f \u092a\u094d\u0930\u0926\u0930\u094d\u0936\u0928 \u0915\u094c\u0936\u0932 \u0915\u094b \u0938\u0941\u0927\u093e\u0930\u0928\u093e \u091a\u093e\u0939\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u092f\u0939 \u0915\u0915\u094d\u0937\u093e \u0906\u092a\u0915\u0947 \u0932\u093f\u090f \u092c\u0939\u0941\u0924 \u0909\u092a\u092f\u094b\u0917\u0940 \u0939\u094b\u0917\u0940\u0964<\/em><\/p>\n<p><\/center><br \/>\n<\/p>\n<p><strong>\u0932\u0930\u094d\u0928\u093f\u0902\u0917 \u0909\u0926\u094d\u0926\u0947\u0936\u094d\u092f:<\/strong><\/p>\n<ol>\n<li><strong>\u0938\u092e\u091d\u0947\u0902<\/strong> \u0938\u0902\u092f\u094b\u091c\u0928 \u0914\u0930 \u0935\u093f\u0938\u0902\u092f\u094b\u091c\u0928 \u0915\u0940 \u0936\u0941\u0930\u0942\u0906\u0924 \u0914\u0930 \u0909\u0928\u094d\u092e\u0942\u0932\u0928 \u0924\u0915\u0928\u0940\u0915\u094b\u0902 \u0915\u0947 \u092a\u0940\u091b\u0947 \u0915\u0940 \u092f\u0941\u0915\u094d\u0924\u093f\u0964<\/li>\n<li><strong>\u0938\u092e\u091d\u0947\u0902<\/strong> \u0915\u094d\u0932\u093e\u0938\u093f\u0915\u0932 \u0932\u0949\u091c\u093f\u0915 \u092e\u0947\u0902 \u0924\u0940\u0938\u0930\u0947 \u0915\u093e \u092c\u0939\u093f\u0937\u094d\u0915\u093e\u0930 \u092f\u093e \u0924\u0930\u094d\u0915\u0935\u093e\u0915\u094d\u092f (TAU) \u0915\u0940 \u0935\u093f\u0936\u0947\u0937\u0924\u093e\u0964<\/li>\n<li><strong>\u0938\u092e\u091d\u0947\u0902<\/strong> \u0915\u094d\u0932\u093e\u0938\u093f\u0915\u0932 \u0932\u0949\u091c\u093f\u0915 \u092e\u0947\u0902 \u0935\u093f\u0930\u094b\u0927\u093e\u092d\u093e\u0938 \u0915\u093e \u0928\u093f\u092f\u092e (CON) \u092f\u093e \u0935\u093f\u0938\u094d\u092b\u094b\u091f \u0915\u093e \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924\u0964<\/li>\n<li><strong>\u0938\u092e\u091d\u0947\u0902<\/strong> \u0915\u094d\u0932\u093e\u0938\u093f\u0915\u0932 \u0932\u0949\u091c\u093f\u0915 \u092e\u0947\u0902 \u0935\u093f\u0938\u0902\u092f\u094b\u091c\u0928 \u0909\u0928\u094d\u092e\u0942\u0932\u0928 \u0924\u0915\u0928\u0940\u0915 (\u2228-\u0909\u0928\u094d\u092e\u0942\u0932\u0928)\u0964<\/li>\n<li><strong>\u0938\u092e\u091d\u0947\u0902<\/strong> \u0915\u094d\u0932\u093e\u0938\u093f\u0915\u0932 \u0932\u0949\u091c\u093f\u0915 \u092e\u0947\u0902 \u092e\u093e\u092e\u0932\u094b\u0902 \u0926\u094d\u0935\u093e\u0930\u093e \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u0940 \u0924\u0915\u0928\u0940\u0915 (CAS)\u0964<\/li>\n<li><strong>\u0938\u092e\u091d\u0947\u0902<\/strong> \u0915\u094d\u0932\u093e\u0938\u093f\u0915\u0932 \u0932\u0949\u091c\u093f\u0915 \u092e\u0947\u0902 \u0905\u092d\u093f\u0936\u093e\u092a \u0924\u0915 \u0909\u0928\u094d\u092e\u0942\u0932\u0928 \u0915\u0940 \u0924\u0915\u0928\u0940\u0915 (absurdo)\u0964<\/li>\n<li><strong>\u0932\u093e\u0917\u0942 \u0915\u0930\u0947\u0902<\/strong> \u0915\u094d\u0932\u093e\u0938\u093f\u0915\u0932 \u0932\u0949\u091c\u093f\u0915 \u0915\u0940 \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0924\u0915\u0928\u0940\u0915\u094b\u0902 \u0915\u0947 \u091c\u094d\u091e\u093e\u0928 \u0915\u094b \u091c\u091f\u093f\u0932 \u0938\u092e\u0938\u094d\u092f\u093e\u0913\u0902 \u0914\u0930 \u092a\u094d\u0930\u0926\u0930\u094d\u0936\u0928 \u0915\u094b \u0939\u0932 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f\u0964<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><strong>\u0938\u0942\u091a\u0915\u093e\u0902\u0915<\/strong><br \/>\n<a href=\"#1\"><strong>\u0938\u0902\u092f\u094b\u091c\u0928 \u0914\u0930 \u0935\u093f\u0938\u0902\u092f\u094b\u091c\u0928 \u0915\u0940 \u0936\u0941\u0930\u0942\u0906\u0924 \u0914\u0930 \u0909\u0928\u094d\u092e\u0942\u0932\u0928<\/strong><\/a><br \/>\n<a href=\"#2\">\u2228-\u0936\u0941\u0930\u0942\u0906\u0924<\/a><br \/>\n<a href=\"#3\">\u2228-\u0909\u0928\u094d\u092e\u0942\u0932\u0928<\/a><br \/>\n<a href=\"#4\">\u2227-\u0936\u0941\u0930\u0942\u0906\u0924<\/a><br \/>\n<a href=\"#5\">\u2227-\u0909\u0928\u094d\u092e\u0942\u0932\u0928<\/a><br \/>\n<a href=\"#6\"><strong>\u0935\u093f\u0930\u094b\u0927\u093e\u092d\u093e\u0938 \u0914\u0930 \u0924\u0930\u094d\u0915\u0935\u093e\u0915\u094d\u092f \u0915\u0940 \u0924\u0915\u0928\u0940\u0915\u0947\u0902<\/strong><\/a><br \/>\n<a href=\"#7\">\u0924\u0940\u0938\u0930\u0947 \u0915\u093e \u092c\u0939\u093f\u0937\u094d\u0915\u093e\u0930 \u092f\u093e \u0924\u0930\u094d\u0915\u0935\u093e\u0915\u094d\u092f (TAU)<\/a><br \/>\n<a href=\"#8\">\u0935\u093f\u0930\u094b\u0927\u093e\u092d\u093e\u0938 \u0915\u093e \u0928\u093f\u092f\u092e \u092f\u093e \u0935\u093f\u0938\u094d\u092b\u094b\u091f \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924<\/a><br \/>\n<a href=\"#9\">\u2228-\u0909\u0928\u094d\u092e\u0942\u0932\u09283<\/a><br \/>\n<a href=\"#10\">\u092e\u093e\u092e\u0932\u094b\u0902 \u0926\u094d\u0935\u093e\u0930\u093e \u092a\u0930\u0940\u0915\u094d\u0937\u0923 (CAS)<\/a><br \/>\n<a href=\"#11\">\u0905\u092d\u093f\u0936\u093e\u092a \u0924\u0915 \u0909\u0928\u094d\u092e\u0942\u0932\u0928 (ABSURDO)<\/a><\/p>\n<p><center><br \/>\n<iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/qAJ_oaSfd9k\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center>\n<\/div>\n<p><a name=\"1\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h2>\u0938\u0902\u092f\u094b\u091c\u0928 \u0914\u0930 \u0935\u093f\u0938\u0902\u092f\u094b\u091c\u0928 \u0915\u0940 \u0936\u0941\u0930\u0942\u0906\u0924 \u0914\u0930 \u0909\u0928\u094d\u092e\u0942\u0932\u0928<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=qAJ_oaSfd9k&amp;t=439s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u0915\u094d\u0932\u093e\u0938\u093f\u0915\u0932 \u0932\u0949\u091c\u093f\u0915 \u0915\u0940 \u090f\u0915 \u0924\u0915\u0928\u0940\u0915<\/span><\/strong><\/a> \u0938\u0902\u092f\u094b\u091c\u0915\u094b\u0902 \u0914\u0930 \u0935\u093f\u0938\u0902\u092f\u094b\u091c\u0915\u094b\u0902 \u0915\u0940 \u0936\u0941\u0930\u0942\u0906\u0924 \u0914\u0930 \u0909\u0928\u094d\u092e\u0942\u0932\u0928 \u0939\u0948\u0964 \u0939\u093e\u0932\u093e\u0902\u0915\u093f \u092f\u0947 \u0924\u0915\u0928\u0940\u0915\u0947\u0902 \u0905\u0927\u093f\u0915 \u092f\u093e \u0915\u092e \u0938\u0939\u091c \u0930\u0942\u092a \u0938\u0947 \u0932\u093e\u0917\u0942 \u0939\u094b\u0924\u0940 \u0939\u0948\u0902, \u0932\u0947\u0915\u093f\u0928 \u0909\u0928\u0915\u093e \u092f\u0941\u0915\u094d\u0924\u093f\u0938\u0902\u0917\u0924\u093f\u0915\u0930\u0923 \u092a\u0942\u0930\u0940 \u0924\u0930\u0939 \u0938\u0947 \u0938\u0930\u0932 \u0928\u0939\u0940\u0902 \u0939\u0948, \u0932\u0947\u0915\u093f\u0928 \u0909\u0928\u094d\u0939\u0947\u0902 \u0939\u092e \u092a\u0939\u0932\u0947 \u0915\u0947 \u0915\u0915\u094d\u0937\u093e\u0913\u0902 \u092e\u0947\u0902 \u092a\u094d\u0930\u092e\u093e\u0923\u093f\u0924 \u0915\u093f\u090f \u0917\u090f \u092a\u094d\u0930\u0938\u094d\u0924\u093e\u0935\u0928\u093e\u0924\u094d\u092e\u0915 \u0932\u0949\u091c\u093f\u0915 \u0915\u0947 \u0928\u093f\u092f\u092e\u094b\u0902 \u0938\u0947 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 \u0914\u092a\u091a\u093e\u0930\u093f\u0915 \u0930\u0942\u092a \u0938\u0947, \u0938\u0902\u092f\u094b\u091c\u0915\u094b\u0902 \u0914\u0930 \u0935\u093f\u0938\u0902\u092f\u094b\u091c\u0915\u094b\u0902 \u0915\u0940 \u0936\u0941\u0930\u0942\u0906\u0924 \u0914\u0930 \u0909\u0928\u094d\u092e\u0942\u0932\u0928 \u0915\u0940 \u0924\u0915\u0928\u0940\u0915\u0947\u0902 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0939\u0948\u0902:<\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td>\u2228-\u0936\u0941\u0930\u0942\u0906\u0924<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\alpha \\} \\vdash (\\alpha \\vee \\beta)<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td>\u2228-\u0909\u0928\u094d\u092e\u0942\u0932\u0928<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha\\vee\\beta), \\neg\\alpha \\} \\vdash\\beta <\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td>\u2227-\u0936\u0941\u0930\u0942\u0906\u0924<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\alpha.\\beta \\} \\vdash(\\alpha \\wedge \\beta) <\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td>\u2227-\u0909\u0928\u094d\u092e\u0942\u0932\u0928<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\wedge \\beta) \\} \\vdash \\alpha <\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\">\u0914\u0930 \u0909\u0928\u0915\u0947 \u092a\u094d\u0930\u0938\u094d\u0924\u093e\u0935\u0928\u093e\u0924\u094d\u092e\u0915 \u0932\u0949\u091c\u093f\u0915 \u0938\u0947 \u092a\u094d\u0930\u092e\u093e\u0923 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0939\u0948\u0902:<\/p>\n<p><a name=\"2\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h3>\u2228-\u0936\u0941\u0930\u0942\u0906\u0924<\/h3>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td>(1)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\alpha\\} \\vdash \\alpha<\/span><\/span><\/td>\n<td>; \u092a\u094d\u0930\u0938\u094d\u0924\u093e\u0935\u0928\u093e<\/td>\n<\/tr>\n<tr>\n<td>(2)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\alpha\\} \\vdash( \\alpha \\rightarrow (\\neg \\beta \\rightarrow \\alpha))<\/span><\/span><\/td>\n<td>; A1, \u090f\u0915\u0930\u0942\u092a\u0924\u093e<\/td>\n<\/tr>\n<tr>\n<td>(3)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\alpha\\} \\vdash (\\neg \\beta \\rightarrow \\alpha)<\/span><\/span><\/td>\n<td>; MP(1,2)<\/td>\n<\/tr>\n<tr>\n<td>(4)<\/td>\n<td><span style=\"color: #880000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\{\\alpha\\} \\vdash (\\beta \\vee \\alpha)}<\/span><\/span><\/span><\/td>\n<td>; <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\rightarrow<\/span><\/span>-\u092a\u0930\u093f\u092d\u093e\u0937\u093e(3)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"3\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h3>\u2228-\u0909\u0928\u094d\u092e\u0942\u0932\u0928<\/h3>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td>(1)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\vee \\beta), \\neg\\alpha\\}\\vdash (\\alpha \\vee\\beta)<\/span><\/span><\/td>\n<td>; \u092a\u094d\u0930\u0938\u094d\u0924\u093e\u0935\u0928\u093e<\/td>\n<\/tr>\n<tr>\n<td>(2)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\vee \\beta), \\neg\\alpha\\}\\vdash \\neg\\alpha <\/span><\/span><\/td>\n<td>; \u092a\u094d\u0930\u0938\u094d\u0924\u093e\u0935\u0928\u093e<\/td>\n<\/tr>\n<tr>\n<td>(3)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\vee \\beta), \\neg\\alpha\\}\\vdash (\\neg \\alpha \\rightarrow \\beta)<\/span><\/span><\/td>\n<td>; <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\rightarrow<\/span><\/span>-\u092a\u0930\u093f\u092d\u093e\u0937\u093e (1)<\/td>\n<\/tr>\n<tr>\n<td>(4)<\/td>\n<td><span style=\"color: #880000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\{(\\alpha \\vee \\beta), \\neg\\alpha\\}\\vdash \\beta}<\/span><\/span><\/span><\/td>\n<td>; MP(2,3)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"4\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h3>\u2227-\u0936\u0941\u0930\u0942\u0906\u0924<\/h3>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td>(1)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\neg\\alpha \\vee \\neg \\beta), \\neg\\neg\\beta\\} \\vdash \\neg\\alpha<\/span><\/span><\/td>\n<td>; <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vee<\/span><\/span>-\u0909\u0928\u094d\u092e\u0942\u0932\u0928<\/td>\n<\/tr>\n<tr>\n<td>(2)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\neg\\neg\\beta\\} \\vdash ((\\neg\\alpha \\vee \\neg \\beta) \\rightarrow \\neg\\alpha)<\/span><\/span><\/td>\n<td>; TD(1)<\/td>\n<\/tr>\n<tr>\n<td>(3)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\neg\\neg\\beta\\} \\vdash (\\neg \\neg\\alpha \\rightarrow \\neg (\\neg\\alpha \\vee \\neg \\beta))<\/span><\/span><\/td>\n<td>; CPI(2))<\/td>\n<\/tr>\n<tr>\n<td>(4)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\vdash (\\neg\\neg\\beta \\rightarrow (\\neg \\neg\\alpha \\rightarrow \\neg (\\neg\\alpha \\vee \\neg \\beta)))<\/span><\/span><\/td>\n<td>; TD(3)<\/td>\n<\/tr>\n<tr>\n<td>(5)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\{\\alpha, \\beta \\} \\vdash (\\neg\\neg\\beta \\rightarrow (\\neg \\neg\\alpha \\rightarrow \\neg (\\neg\\alpha \\vee \\neg \\beta)))<\/span><\/span><\/td>\n<td>; \u090f\u0915\u0930\u0942\u092a\u0924\u093e x2 (4)<\/td>\n<\/tr>\n<tr>\n<td>(6)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\{\\alpha, \\beta \\} \\vdash \\beta<\/span><\/span><\/td>\n<td>; \u092a\u094d\u0930\u0938\u094d\u0924\u093e\u0935\u0928\u093e<\/td>\n<\/tr>\n<tr>\n<td>(7)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\{\\alpha, \\beta \\} \\vdash \\neg\\neg\\beta<\/span><\/span><\/td>\n<td>; DN(6)<\/td>\n<\/tr>\n<tr>\n<td>(8)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\{\\alpha, \\beta \\} \\vdash (\\neg \\neg\\alpha \\rightarrow \\neg (\\neg\\alpha \\vee \\neg \\beta))<\/span><\/span><\/td>\n<td>; MP(7,5)<\/td>\n<\/tr>\n<tr>\n<td>(9)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\{\\alpha, \\beta \\} \\vdash \\alpha<\/span><\/span><\/td>\n<td>; \u092a\u094d\u0930\u0938\u094d\u0924\u093e\u0935\u0928\u093e<\/td>\n<\/tr>\n<tr>\n<td>(10)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\{\\alpha, \\beta \\} \\vdash \\neg\\neg\\alpha<\/span><\/span><\/td>\n<td>; DN(9)<\/td>\n<\/tr>\n<tr>\n<td>(11)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\{\\alpha, \\beta \\} \\vdash \\neg (\\neg\\alpha \\vee \\neg \\beta)<\/span><\/span><\/td>\n<td>; MP(10,8)<\/td>\n<\/tr>\n<tr>\n<td>(12)<\/td>\n<td><span style=\"color: #880000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\{\\alpha, \\beta \\} \\vdash (\\alpha \\wedge \\beta)}<\/span><\/span><\/span><\/td>\n<td>; <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\wedge<\/span><\/span>-\u092a\u0930\u093f\u092d\u093e\u0937\u093e(11)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"5\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h3>\u2227-\u0909\u0928\u094d\u092e\u0942\u0932\u0928<\/h3>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td>(1)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\wedge \\beta)\\} \\vdash (\\alpha \\wedge \\beta)<\/span><\/span><\/td>\n<td>; \u092a\u094d\u0930\u0938\u094d\u0924\u093e\u0935\u0928\u093e<\/td>\n<\/tr>\n<tr>\n<td>(2)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\neg \\alpha\\} \\vdash (\\neg \\alpha \\vee \\neg\\beta)<\/span><\/span><\/td>\n<td>; <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vee<\/span><\/span>-\u0936\u0941\u0930\u0942\u0906\u0924<\/td>\n<\/tr>\n<tr>\n<td>(3)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\vdash (\\neg \\alpha \\rightarrow (\\neg \\alpha \\vee \\neg\\beta))<\/span><\/span><\/td>\n<td>; TD(2)<\/td>\n<\/tr>\n<tr>\n<td>(4)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\vdash (\\neg(\\neg \\alpha \\vee \\neg\\beta) \\rightarrow \\alpha)<\/span><\/span><\/td>\n<td>; CPI(3))<\/td>\n<\/tr>\n<tr>\n<td>(5)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\vdash ( ( \\alpha \\wedge \\beta) \\rightarrow \\alpha)<\/span><\/span><\/td>\n<td>; <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\wedge<\/span><\/span>-\u092a\u0930\u093f\u092d\u093e\u0937\u093e(4)<\/td>\n<\/tr>\n<tr>\n<td>(6)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\{(\\alpha \\wedge \\beta)\\} \\vdash ( ( \\alpha \\wedge \\beta) \\rightarrow \\alpha)<\/span><\/span><\/td>\n<td>; \u090f\u0915\u0930\u0942\u092a\u0924\u093e(5)<\/td>\n<\/tr>\n<tr>\n<td>(7)<\/td>\n<td><span style=\"color: #880000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\{(\\alpha \\wedge \\beta)\\} \\vdash \\alpha}<\/span><\/span><\/span><\/td>\n<td>; MP(1,6)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"6\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h2>\u0935\u093f\u0930\u094b\u0927\u093e\u092d\u093e\u0938 \u0914\u0930 \u0924\u0930\u094d\u0915\u0935\u093e\u0915\u094d\u092f \u0915\u0940 \u0924\u0915\u0928\u0940\u0915\u0947\u0902<\/h2>\n<p><a name=\"7\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h3>\u0924\u0940\u0938\u0930\u0947 \u0915\u093e \u092c\u0939\u093f\u0937\u094d\u0915\u093e\u0930 \u092f\u093e \u0924\u0930\u094d\u0915\u0935\u093e\u0915\u094d\u092f (tau)<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=qAJ_oaSfd9k&amp;t=1208s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u0915\u094d\u0932\u093e\u0938\u093f\u0915\u0932 \u0932\u0949\u091c\u093f\u0915 \u0915\u093e \u090f\u0915 \u0914\u0930 \u0935\u093f\u0936\u093f\u0937\u094d\u091f \u0917\u0941\u0923<\/span><\/strong><\/a> \u0924\u0940\u0938\u0930\u0947 \u0915\u093e \u092c\u0939\u093f\u0937\u094d\u0915\u093e\u0930 (tertium non datur) \u0915\u0940 \u0935\u093f\u0936\u0947\u0937\u0924\u093e \u0939\u0948\u0964 \u092f\u0939 \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 \u0915\u093f \u092f\u0926\u093f \u0926\u094b \u0915\u0925\u0928 \u0939\u0948\u0902, \u091c\u093f\u0928\u092e\u0947\u0902 \u0938\u0947 \u090f\u0915 \u0926\u0942\u0938\u0930\u0947 \u0915\u093e \u0916\u0902\u0921\u0928 \u0915\u0930\u0924\u093e \u0939\u0948, \u0924\u094b \u0909\u0928\u092e\u0947\u0902 \u0938\u0947 \u090f\u0915 \u0938\u0924\u094d\u092f \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f; \u092f\u093e \u0926\u0942\u0938\u0930\u0947 \u0936\u092c\u094d\u0926\u094b\u0902 \u092e\u0947\u0902, \u0926\u094b \u0915\u0925\u0928\u094b\u0902 \u0915\u093e \u0938\u0902\u092f\u094b\u091c\u0928 \u091c\u093f\u0938\u092e\u0947\u0902 \u090f\u0915 \u0926\u0942\u0938\u0930\u0947 \u0915\u093e \u0916\u0902\u0921\u0928 \u0915\u0930\u0924\u093e \u0939\u0948, \u0905\u0928\u093f\u0935\u093e\u0930\u094d\u092f \u0930\u0942\u092a \u0938\u0947 \u0924\u0930\u094d\u0915\u0935\u093e\u0915\u094d\u092f \u092c\u0928\u093e\u0924\u093e \u0939\u0948\u0964 \u0914\u092a\u091a\u093e\u0930\u093f\u0915 \u0930\u0942\u092a \u0938\u0947, \u0907\u0938\u0947 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0932\u093f\u0916\u093e \u091c\u093e\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vdash (\\neg\\alpha \\vee\\alpha)<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0914\u0930 \u0907\u0938\u0915\u093e \u092a\u094d\u0930\u092e\u093e\u0923 \u0906\u0938\u093e\u0928\u0940 \u0938\u0947 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964<\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td>(1)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\alpha\\}\\vdash \\alpha<\/span><\/span><\/td>\n<td>; \u092a\u094d\u0930\u0938\u094d\u0924\u093e\u0935\u0928\u093e<\/td>\n<\/tr>\n<tr>\n<td>(2)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vdash (\\alpha \\rightarrow \\alpha)<\/span><\/span><\/td>\n<td>; TD(1)<\/td>\n<\/tr>\n<tr>\n<td>(3)<\/td>\n<td><span style=\"color: #880000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\vdash (\\neg \\alpha \\vee \\alpha)}<\/span><\/span><\/span><\/td>\n<td>; \u0938\u0947 (2) \u0915\u094d\u092f\u094b\u0902\u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha \\rightarrow \\beta) := (\\neg \\alpha \\vee \\beta)<\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\">\u0924\u0940\u0938\u0930\u0947 \u0915\u093e \u092c\u0939\u093f\u0937\u094d\u0915\u093e\u0930 \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 \u0915\u0940 \u090f\u0915 \u0914\u0930 \u0935\u093f\u0927\u093f \u0939\u0948 <strong>\u0935\u093f\u0930\u094b\u0927\u093e\u092d\u093e\u0938 \u0915\u093e \u0928\u093f\u092f\u092e<\/strong>, \u091c\u094b \u092f\u0939 \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 \u0915\u093f \u090f\u0915 \u0915\u0925\u0928 \u090f\u0915 \u0939\u0940 \u0938\u092e\u092f \u092e\u0947\u0902 \u0938\u0924\u094d\u092f \u0914\u0930 \u0905\u0938\u0924\u094d\u092f \u0928\u0939\u0940\u0902 \u0939\u094b \u0938\u0915\u0924\u093e \u0914\u0930 \u0914\u092a\u091a\u093e\u0930\u093f\u0915 \u0930\u0942\u092a \u0938\u0947 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0935\u094d\u092f\u0915\u094d\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vdash \\neg(\\neg\\alpha \\wedge \\alpha)<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0907\u0938 \u0917\u0941\u0923 \u0915\u094b \u092a\u094d\u0930\u092e\u093e\u0923 \u0915\u0940 \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e \u0928\u0939\u0940\u0902 \u0939\u0948, \u0928 \u0915\u0947\u0935\u0932 \u0907\u0938\u0932\u093f\u090f \u0915\u093f \u092f\u0939 \u0938\u094d\u0935\u092f\u0902\u0938\u093f\u0926\u094d\u0927 \u0939\u0948, \u092c\u0932\u094d\u0915\u093f \u0907\u0938\u0932\u093f\u090f \u0915\u093f \u092f\u0939 \u0938\u0940\u0927\u0947 \u0924\u0940\u0938\u0930\u0947 \u0915\u093e \u092c\u0939\u093f\u0937\u094d\u0915\u093e\u0930 \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 \u092a\u0930 \u0938\u0902\u092f\u094b\u0917 \u0915\u0947 \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u0915\u094b \u0932\u093e\u0917\u0942 \u0915\u0930\u0928\u0947 \u0938\u0947 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u0940 \u0939\u0948\u0964<\/p>\n<p><a name=\"8\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h3>\u0935\u093f\u0930\u094b\u0927\u093e\u092d\u093e\u0938 \u0915\u093e \u0928\u093f\u092f\u092e \u092f\u093e \u0935\u093f\u0938\u094d\u092b\u094b\u091f \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=qAJ_oaSfd9k&amp;t=1410s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u0915\u094d\u0932\u093e\u0938\u093f\u0915\u0932 \u0932\u0949\u091c\u093f\u0915 \u0915\u093e \u090f\u0915 \u0914\u0930 \u091c\u093e\u0928\u093e-\u092e\u093e\u0928\u093e \u0917\u0941\u0923<\/span><\/strong><\/a> \u0935\u093f\u0938\u094d\u092b\u094b\u091f \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 \u0939\u0948, \u091c\u093f\u0938\u0947 \u0906\u092e\u0924\u094c\u0930 \u092a\u0930 \u00ab\u0935\u093f\u0930\u094b\u0927\u093e\u092d\u093e\u0938\u0940 \u092a\u094d\u0930\u0938\u094d\u0925\u093e\u0928 \u0938\u0947 \u0915\u0941\u091b \u092d\u0940 \u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937 \u0928\u093f\u0915\u093e\u0932\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u00bb \u0935\u093e\u0915\u094d\u092f\u093e\u0902\u0936 \u0926\u094d\u0935\u093e\u0930\u093e \u0935\u094d\u092f\u0915\u094d\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0907\u0938\u0915\u0940 \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924\u093f \u0906\u092e\u0924\u094c\u0930 \u092a\u0930 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0926\u094b \u0924\u0930\u0940\u0915\u094b\u0902 \u092e\u0947\u0902 \u0938\u0947 \u0915\u093f\u0938\u0940 \u090f\u0915 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u0939\u094b\u0924\u0940 \u0939\u0948:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\neg\\alpha \\wedge \\alpha)\\}\\vdash \\beta<\/span><\/span><\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\alpha, \\neg\\alpha\\}\\vdash \\beta<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0907\u0938 \u0928\u093f\u092f\u092e \u0915\u093e \u092a\u094d\u0930\u092e\u093e\u0923 \u0938\u0930\u0932 \u0939\u0948:<\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td>(1)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\alpha ,\\neg\\alpha\\} \\vdash \\neg\\alpha <\/span><\/span><\/td>\n<td>; \u092a\u094d\u0930\u0938\u094d\u0924\u093e\u0935\u0928\u093e<\/td>\n<\/tr>\n<tr>\n<td>(2)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\alpha ,\\neg\\alpha\\} \\vdash (\\neg\\alpha \\vee \\beta) <\/span><\/span><\/td>\n<td>; <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vee<\/span><\/span>-\u0936\u0941\u0930\u0942\u0906\u0924<\/td>\n<\/tr>\n<tr>\n<td>(3)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\alpha ,\\neg\\alpha\\} \\vdash (\\alpha \\rightarrow \\beta) <\/span><\/span><\/td>\n<td>; <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\rightarrow<\/span><\/span>-\u092a\u0930\u093f\u092d\u093e\u0937\u093e(2)<\/td>\n<\/tr>\n<tr>\n<td>(4)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\alpha ,\\neg\\alpha\\} \\vdash \\alpha <\/span><\/span><\/td>\n<td>; \u092a\u094d\u0930\u0938\u094d\u0924\u093e\u0935\u0928\u093e<\/td>\n<\/tr>\n<tr>\n<td>(5)<\/td>\n<td><span style=\"color: #880000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\{\\alpha ,\\neg\\alpha\\} \\vdash \\beta}<\/span><\/span><\/span><\/td>\n<td>; MP(4,3)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"9\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h3>\u2228-\u0909\u0928\u094d\u092e\u0942\u0932\u09283<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=qAJ_oaSfd9k&amp;t=1555s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u0924\u093e\u0930\u094d\u0915\u093f\u0915 \u0928\u093f\u092f\u092e\u093e\u0928\u0941\u0938\u093e\u0930 (modus ponens) \u0915\u094b \u0926\u094b \u0905\u0932\u0917-\u0905\u0932\u0917 \u0924\u0930\u0940\u0915\u094b\u0902 \u0938\u0947 \u0932\u093f\u0916\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948<\/span><\/strong><\/a>. \u0939\u092e\u0947\u0902 \u092a\u0939\u0932\u0947 \u0938\u0947 \u0939\u0940 \u091c\u094d\u091e\u093e\u0924 \u090f\u0915 \u0924\u0930\u0940\u0915\u093e \u0939\u0948<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\alpha,(\\alpha \\rightarrow \\beta)\\}\\vdash \\beta<\/span><\/span>. \u0926\u0942\u0938\u0930\u093e \u0924\u0930\u0940\u0915\u093e \u0925\u094b\u0921\u093c\u093e \u0915\u092e \u092a\u0930\u093f\u091a\u093f\u0924 \u0939\u0948:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\alpha\\}\\vdash\\beta \\; \\wedge \\; \\vdash \\alpha \\; \\Longrightarrow \\; \\vdash \\beta<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0907\u0938 \u0926\u0942\u0938\u0930\u0947 \u0924\u0930\u0940\u0915\u0947 \u092a\u0930 \u0927\u094d\u092f\u093e\u0928 \u0915\u0947\u0902\u0926\u094d\u0930\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0941\u090f, \u0939\u092e \u0907\u0938 \u0928\u093f\u092f\u092e \u0915\u093e \u090f\u0915 \u0935\u093f\u0938\u094d\u0924\u093e\u0930 \u0926\u0947\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u091c\u093f\u0938\u0947 \u0939\u092e <strong>\u2228-\u0909\u0928\u094d\u092e\u0942\u0932\u09283<\/strong> \u0915\u0939\u0924\u0947 \u0939\u0948\u0902, \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u092f\u0939 \u090f\u0915 \u0935\u093f\u0938\u0902\u092f\u094b\u091c\u0928 \u0938\u0947 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0938\u0930\u0932\u0940\u0915\u0930\u0923 \u0915\u0947 \u0938\u092e\u093e\u0928 \u0939\u0948\u0964 \u092f\u0939 \u0939\u092e\u0947\u0902 \u092c\u0924\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u092f\u0926\u093f<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\gamma<\/span><\/span> \u0915\u094b<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span> \u0914\u0930<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\beta<\/span><\/span> \u0938\u0947 (\u0926\u094b\u0928\u094b\u0902 \u0938\u0947 \u090f\u0915 \u0938\u093e\u0925) \u0914\u0930 \u092f\u0926\u093f<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span> \u0914\u0930<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\beta<\/span><\/span> \u0915\u0947 \u092c\u0940\u091a \u0915\u093e \u0935\u093f\u0938\u0902\u092f\u094b\u091c\u0928 \u090f\u0915 \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 \u0939\u0948, \u0924\u094b<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\gamma<\/span><\/span> \u090f\u0915 \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 \u0939\u0948\u0964 \u0907\u0938\u0947 \u0914\u092a\u091a\u093e\u0930\u093f\u0915 \u0930\u0942\u092a \u0938\u0947 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0932\u093f\u0916\u093e \u091c\u093e\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span style=\"color: #880000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\{\\alpha\\}\\vdash\\gamma\\; \\wedge \\; \\{\\beta\\}\\vdash\\gamma \\; \\wedge \\; \\vdash (\\alpha \\vee \\beta)<\/span><\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Longrightarrow<\/span><\/span> <span style=\"color: #000088;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vdash \\gamma<\/span><\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0907\u0938 \u0915\u094d\u0932\u093e\u0938\u093f\u0915\u0932 \u0932\u0949\u091c\u093f\u0915 \u0924\u0915\u0928\u0940\u0915 \u0915\u093e \u092a\u094d\u0930\u092e\u093e\u0923 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0939\u0948:<\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td>(1)<\/td>\n<td><span style=\"color: #880000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\alpha \\vdash \\gamma}<\/span><\/span><\/span><\/td>\n<td>; \u092a\u094d\u0930\u0938\u094d\u0924\u093e\u0935\u0928\u093e<\/td>\n<\/tr>\n<tr>\n<td>(2)<\/td>\n<td><span style=\"color: #880000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\beta \\vdash \\gamma}<\/span><\/span><\/td>\n<td>; \u092a\u094d\u0930\u0938\u094d\u0924\u093e\u0935\u0928\u093e<\/td>\n<\/tr>\n<tr>\n<td>(3)<\/td>\n<td><span style=\"color: #880000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\vdash (\\alpha \\vee \\beta)}<\/span><\/span><\/td>\n<td>; \u092a\u094d\u0930\u0938\u094d\u0924\u093e\u0935\u0928\u093e<\/td>\n<\/tr>\n<tr>\n<td>(4)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\vdash (\\alpha \\rightarrow \\gamma)<\/span><\/span><\/td>\n<td>; TD(1)<\/td>\n<\/tr>\n<tr>\n<td>(5)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\vdash (\\beta \\rightarrow \\gamma)<\/span><\/span><\/td>\n<td>; TD(2)<\/td>\n<\/tr>\n<tr>\n<td>(6)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\vdash (\\neg \\gamma \\rightarrow \\neg \\alpha)<\/span><\/span><\/td>\n<td>; CPI(4)<\/td>\n<\/tr>\n<tr>\n<td>(7)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\vdash (\\neg \\gamma \\rightarrow \\neg \\beta)<\/span><\/span><\/td>\n<td>; CPI(5)<\/td>\n<\/tr>\n<tr>\n<td>(8)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\{\\neg \\gamma \\}\\vdash \\neg \\alpha<\/span><\/span><\/td>\n<td>; RTD(6)<\/td>\n<\/tr>\n<tr>\n<td>(9)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\{\\neg \\gamma\\}\\vdash \\neg \\beta<\/span><\/span><\/td>\n<td>; RTD(7)<\/td>\n<\/tr>\n<tr>\n<td>(10)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\{\\neg \\gamma\\}\\vdash (\\neg \\alpha \\wedge \\neg \\beta)<\/span><\/span><\/td>\n<td>; <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\wedge<\/span><\/span>-\u0936\u0941\u0930\u0942\u0906\u0924(8,9)<\/td>\n<\/tr>\n<tr>\n<td>(11)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\vdash (\\neg \\gamma \\rightarrow (\\neg \\alpha \\wedge \\neg \\beta))<\/span><\/span><\/td>\n<td>; TD(10)<\/td>\n<\/tr>\n<tr>\n<td>(12)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\vdash (\\neg(\\neg \\alpha \\wedge \\neg \\beta)\\rightarrow \\gamma )<\/span><\/span><\/td>\n<td>; CPI(11)<\/td>\n<\/tr>\n<tr>\n<td>(13)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> (A \\wedge B) := \\neg(\\neg A \\vee \\neg B)<\/span><\/span><\/td>\n<td>; <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\wedge<\/span><\/span> &#8211; \u092a\u0930\u093f\u092d\u093e\u0937\u093e<\/td>\n<\/tr>\n<tr>\n<td>(14)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\neg(A \\wedge B) := \\neg\\neg(\\neg A \\vee \\neg B)<\/span><\/span><\/td>\n<td>; \u0926\u094b\u0928\u094b\u0902 \u092a\u0915\u094d\u0937\u094b\u0902 \u0915\u094b \u0928\u0915\u093e\u0930\u0928\u093e (13)<\/td>\n<\/tr>\n<tr>\n<td>(15)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\neg(\\neg\\alpha \\wedge \\neg\\beta) := \\neg\\neg(\\neg\\neg\\alpha \\vee \\neg\\neg\\beta)<\/span><\/span><\/td>\n<td>; \u092a\u094d\u0930\u0924\u093f\u0938\u094d\u0925\u093e\u092a\u0928 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">A:=\\neg\\alpha<\/span><\/span> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">B:=\\neg\\beta<\/span><\/span> \u092e\u0947\u0902 (14)<\/td>\n<\/tr>\n<tr>\n<td>(16)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\neg(\\neg\\alpha \\wedge \\neg\\beta) \\dashv \\vdash (\\alpha \\vee \\beta)<\/span><\/span><\/td>\n<td>; DN(15)<\/td>\n<\/tr>\n<tr>\n<td>(17)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\vdash ((\\alpha \\vee \\beta) \\rightarrow \\neg(\\neg\\alpha \\wedge \\neg\\beta) )<\/span><\/span><\/td>\n<td>; TD(16)<\/td>\n<\/tr>\n<tr>\n<td>(17)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\vdash ((\\alpha \\vee \\beta) \\rightarrow \\gamma )<\/span><\/span><\/td>\n<td>; SH(17,12)<\/td>\n<\/tr>\n<tr>\n<td>(18)<\/td>\n<td><span style=\"color: #000088;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{ \\vdash \\gamma}<\/span><\/span><\/span><\/td>\n<td>; MP(3,17)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"10\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h3>\u092e\u093e\u092e\u0932\u094b\u0902 \u0926\u094d\u0935\u093e\u0930\u093e \u092a\u0930\u0940\u0915\u094d\u0937\u0923 (cas)<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=qAJ_oaSfd9k&amp;t=1957s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\">\u0915\u094d\u0932\u093e\u0938\u093f\u0915\u0932 \u0932\u0949\u091c\u093f\u0915 \u0915\u0940 \u090f\u0915 \u0914\u0930 \u0924\u0915\u0928\u0940\u0915<\/span><\/a> \u092e\u093e\u092e\u0932\u094b\u0902 \u0926\u094d\u0935\u093e\u0930\u093e \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0939\u0948\u0964 \u092f\u0926\u093f \u090f\u0915 \u0905\u092d\u093f\u0935\u094d\u092f\u0915\u094d\u0924\u093f<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\beta<\/span><\/span> \u0915\u094b \u0926\u0942\u0938\u0930\u0940 \u0905\u092d\u093f\u0935\u094d\u092f\u0915\u094d\u0924\u093f<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span> \u0914\u0930 \u0909\u0938\u0915\u0947 \u0928\u093f\u0937\u0947\u0927 \u0926\u094b\u0928\u094b\u0902 \u0938\u0947 \u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937 \u0928\u093f\u0915\u093e\u0932\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948, \u0924\u094b \u0905\u092d\u093f\u0935\u094d\u092f\u0915\u094d\u0924\u093f<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\beta<\/span><\/span> \u0905\u0928\u093f\u0935\u093e\u0930\u094d\u092f \u0930\u0942\u092a \u0938\u0947 \u090f\u0915 \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 \u0939\u0948\u0964 \u0907\u0938\u0947 \u0914\u092a\u091a\u093e\u0930\u093f\u0915 \u0930\u0942\u092a \u0938\u0947 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0932\u093f\u0916\u093e \u091c\u093e\u0924\u093e \u0939\u0948: <span style=\"color: #880000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha \\vdash \\beta \\; \\wedge \\; \\neg\\alpha \\vdash \\beta <\/span><\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Longrightarrow<\/span><\/span> <span style=\"color: #000088;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vdash \\beta<\/span><\/span><\/span>. \u0907\u0938\u0915\u093e \u092a\u094d\u0930\u092e\u093e\u0923 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0939\u0948:<\/p>\n<p style=\"color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rll}\n\n(1) &amp; \\alpha \\vdash \\beta &amp;; \u092a\u094d\u0930\u0938\u094d\u0924\u093e\u0935\u0928\u093e\\\\\n\n(2) &amp; \\neg \\alpha \\vdash \\beta &amp;; \u092a\u094d\u0930\u0938\u094d\u0924\u093e\u0935\u0928\u093e \\\\\n\n(3) &amp; \\vdash \\alpha \\vee \\neg\\alpha &amp;; TAU \\\\\n\n(4) &amp; \\vdash \\beta &amp;; \\vee-\u0909\u0928\u094d\u092e\u0942\u0932\u09283(1,2,3)\n\n\\end{array}\n\n<\/span><\/span><\/p>\n<p><a name=\"11\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h3>\u0905\u092d\u093f\u0936\u093e\u092a \u0924\u0915 \u0909\u0928\u094d\u092e\u0942\u0932\u0928 (absurdo)<\/h3>\n<p style=\"text-align: justify; color: #000000;\">\u0915\u094d\u0932\u093e\u0938\u093f\u0915\u0932 \u0932\u0949\u091c\u093f\u0915 \u0915\u0940 \u0938\u092c\u0938\u0947 \u0905\u0927\u093f\u0915 \u092a\u094d\u0930\u092f\u0941\u0915\u094d\u0924 \u0924\u0915\u0928\u0940\u0915\u094b\u0902 \u092e\u0947\u0902 \u0938\u0947 \u090f\u0915, \u0935\u093f\u0936\u0947\u0937 \u0930\u0942\u092a \u0938\u0947 \u0917\u0923\u093f\u0924 \u092e\u0947\u0902, \u0905\u092d\u093f\u0936\u093e\u092a \u0924\u0915 \u0909\u0928\u094d\u092e\u0942\u0932\u0928 \u0939\u0948\u0964 \u0907\u0938\u0915\u093e \u0905\u0930\u094d\u0925 \u0939\u0948 \u0915\u093f \u092f\u0926\u093f \u090f\u0915 \u0905\u092d\u093f\u0935\u094d\u092f\u0915\u094d\u0924\u093f<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span> \u0938\u0947 \u090f\u0915 \u0935\u093f\u0930\u094b\u0927\u093e\u092d\u093e\u0938 (\u090f\u0915 \u0915\u0925\u0928 \u0914\u0930 \u0909\u0938\u0915\u093e \u0928\u093f\u0937\u0947\u0927) \u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937 \u0928\u093f\u0915\u093e\u0932\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u0924\u094b<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span> \u0915\u093e \u0928\u093f\u0937\u0947\u0927 \u090f\u0915 \u0924\u0930\u094d\u0915\u0935\u093e\u0915\u094d\u092f \u0939\u0948\u0964 \u0914\u092a\u091a\u093e\u0930\u093f\u0915 \u0930\u0942\u092a \u0938\u0947 \u0907\u0938\u0947 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0935\u094d\u092f\u0915\u094d\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948: <span style=\"color: #880000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\alpha\\}\\vdash \\beta \\; \\wedge \\; \\{\\alpha\\}\\vdash \\neg\\beta<\/span><\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Longrightarrow<\/span><\/span> <span style=\"color: #000088;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vdash \\neg\\alpha<\/span><\/span><\/span>. \u0907\u0938\u0915\u093e \u092a\u094d\u0930\u092e\u093e\u0923 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0939\u0948:<\/p>\n<table style=\"color: #000000;\">\n<tbody>\n<tr>\n<td>(1)<\/td>\n<td><span style=\"color: #880000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\{\\alpha\\}\\vdash \\beta}<\/span><\/span><\/span><\/td>\n<td>; \u092a\u094d\u0930\u0938\u094d\u0924\u093e\u0935\u0928\u093e<\/td>\n<\/tr>\n<tr>\n<td>(2)<\/td>\n<td><span style=\"color: #880000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\{\\alpha\\}\\vdash \\neg\\beta}<\/span><\/span><\/td>\n<td>; \u092a\u094d\u0930\u0938\u094d\u0924\u093e\u0935\u0928\u093e<\/td>\n<\/tr>\n<tr>\n<td>(3)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vdash (\\alpha \\rightarrow \\beta)<\/span><\/span><\/td>\n<td>; TD(1)<\/td>\n<\/tr>\n<tr>\n<td>(4)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vdash (\\alpha \\rightarrow \\neg\\beta)<\/span><\/span><\/td>\n<td>; TD(2)<\/td>\n<\/tr>\n<tr>\n<td>(5)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vdash (\\neg \\beta \\rightarrow \\neg \\alpha)<\/span><\/span><\/td>\n<td>; CPI(3)<\/td>\n<\/tr>\n<tr>\n<td>(6)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vdash (\\beta \\rightarrow \\neg \\alpha)<\/span><\/span><\/td>\n<td>; CPI(4)<\/td>\n<\/tr>\n<tr>\n<td>(7)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\neg \\beta \\}\\vdash \\neg \\alpha<\/span><\/span><\/td>\n<td>; RTD(5)<\/td>\n<\/tr>\n<tr>\n<td>(8)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\beta \\}\\vdash \\neg \\alpha<\/span><\/span><\/td>\n<td>; RTD(6)<\/td>\n<\/tr>\n<tr>\n<td>(9)<\/td>\n<td><span style=\"color: #000088;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\vdash \\neg \\alpha}<\/span><\/span><\/span><\/td>\n<td>; CAS(7,8)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>\u0915\u094d\u0932\u093e\u0938\u093f\u0915\u0932 \u0932\u0949\u091c\u093f\u0915 \u0924\u0915\u0928\u0940\u0915\u094b\u0902 \u0915\u093e \u092a\u094d\u0930\u0926\u0930\u094d\u0936\u0928 \u0938\u093e\u0930\u093e\u0902\u0936\u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u0938\u0902\u092f\u094b\u091c\u0928 \u0914\u0930 \u0935\u093f\u0938\u0902\u092f\u094b\u091c\u0928 \u0915\u0940 \u0936\u0941\u0930\u0942\u0906\u0924 \u0914\u0930 \u0909\u0928\u094d\u092e\u0942\u0932\u0928 \u0915\u0947 \u0932\u093f\u090f \u0915\u0908 \u0915\u094d\u0932\u093e\u0938\u093f\u0915\u0932 \u0932\u0949\u091c\u093f\u0915 \u0924\u0915\u0928\u0940\u0915\u094b\u0902 \u0915\u094b \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948, \u0938\u093e\u0925 \u0939\u0940 \u0924\u0940\u0938\u0930\u0947 \u0915\u093e \u092c\u0939\u093f\u0937\u094d\u0915\u093e\u0930 \u0914\u0930 \u0935\u093f\u0938\u094d\u092b\u094b\u091f \u0915\u0947 \u0928\u093f\u092f\u092e \u0915\u094b \u092d\u0940 \u0938\u092e\u091d\u093e\u092f\u093e \u0917\u092f\u093e \u0939\u0948, \u091c\u093f\u0938\u0947 \u0935\u093f\u0930\u094b\u0927\u093e\u092d\u093e\u0938 \u0915\u0947 \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u092d\u0940 \u091c\u093e\u0928\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0907\u0938\u0915\u0947 \u0905\u0932\u093e\u0935\u093e, \u092e\u093e\u092e\u0932\u094b\u0902 \u0926\u094d\u0935\u093e\u0930\u093e [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":27451,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":0,"footnotes":""},"categories":[577,613,627],"tags":[],"class_list":["post-27470","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-577","category-613","category-627"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u0915\u094d\u0932\u093e\u0938\u093f\u0915\u0932 \u0932\u0949\u091c\u093f\u0915 \u0924\u0915\u0928\u0940\u0915\u094b\u0902 \u0915\u093e \u092a\u094d\u0930\u0926\u0930\u094d\u0936\u0928 - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u0915\u094d\u0932\u093e\u0938\u093f\u0915\u0932 \u0932\u0949\u091c\u093f\u0915: \u0938\u0902\u092f\u094b\u091c\u0928 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