{"id":27468,"date":"2021-02-12T13:00:49","date_gmt":"2021-02-12T13:00:49","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=27468"},"modified":"2024-07-09T04:54:12","modified_gmt":"2024-07-09T04:54:12","slug":"%d8%b9%d8%b1%d8%b6-%d8%aa%d9%82%d9%86%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d9%85%d9%86%d8%b7%d9%82-%d8%a7%d9%84%d9%83%d9%84%d8%a7%d8%b3%d9%8a%d9%83%d9%8a","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/ar\/%d8%b9%d8%b1%d8%b6-%d8%aa%d9%82%d9%86%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d9%85%d9%86%d8%b7%d9%82-%d8%a7%d9%84%d9%83%d9%84%d8%a7%d8%b3%d9%8a%d9%83%d9%8a\/","title":{"rendered":"\u0639\u0631\u0636 \u062a\u0642\u0646\u064a\u0627\u062a \u0627\u0644\u0645\u0646\u0637\u0642 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>\u0639\u0631\u0636 \u062a\u0642\u0646\u064a\u0627\u062a \u0627\u0644\u0645\u0646\u0637\u0642 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a<\/h1>\n<p><\/p>\n<p style=\"text-align:center;\"><strong>\u0645\u0644\u062e\u0635<\/strong><br \/><em>\u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629\u060c \u0646\u0642\u062f\u0645 \u0639\u062f\u0629 \u062a\u0642\u0646\u064a\u0627\u062a \u0644\u0644\u0645\u0646\u0637\u0642 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a \u0644\u0625\u062f\u062e\u0627\u0644 \u0648\u0625\u0632\u0627\u0644\u0629 \u0627\u0644\u0627\u0642\u062a\u0631\u0627\u0646\u0627\u062a \u0648\u0627\u0644\u0627\u0646\u0641\u0635\u0627\u0644\u0627\u062a\u060c \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0642\u0627\u0646\u0648\u0646 \u0627\u0644\u062b\u0627\u0644\u062b \u0627\u0644\u0645\u0633\u062a\u0628\u0639\u062f \u0648\u0642\u0627\u0646\u0648\u0646 \u0627\u0644\u062a\u0646\u0627\u0642\u0636\u060c \u0627\u0644\u0645\u0639\u0631\u0648\u0641 \u0623\u064a\u0636\u064b\u0627 \u0628\u0645\u0628\u062f\u0623 \u0627\u0644\u0627\u0646\u0641\u062c\u0627\u0631. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0646\u0634\u0631\u062d \u062a\u0642\u0646\u064a\u0629 \u0627\u0644\u0625\u062b\u0628\u0627\u062a \u0628\u0627\u0644\u062d\u0627\u0644\u0627\u062a \u0648\u062a\u0642\u0646\u064a\u0629 \u0627\u0644\u062a\u0642\u0644\u064a\u0644 \u0625\u0644\u0649 \u0627\u0644\u0639\u0628\u062b\u060c \u0648\u0643\u0644\u0627\u0647\u0645\u0627 \u0645\u0641\u064a\u062f \u062c\u062f\u064b\u0627 \u0641\u064a \u0627\u0644\u0628\u0631\u0627\u0647\u064a\u0646 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u0648\u0627\u0644\u0645\u0646\u0637\u0642\u064a\u0629 \u0628\u0634\u0643\u0644 \u0639\u0627\u0645. \u064a\u062a\u0645 \u062a\u0642\u062f\u064a\u0645 \u0643\u0644 \u062a\u0642\u0646\u064a\u0629 \u0628\u0634\u0643\u0644 \u0631\u0633\u0645\u064a \u0648\u064a\u062a\u0645 \u062a\u0648\u0641\u064a\u0631 \u0628\u0631\u0647\u0627\u0646 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629 \u0644\u0641\u0647\u0645\u0647\u0627. \u0625\u0630\u0627 \u0643\u0646\u062a \u062a\u0631\u063a\u0628 \u0641\u064a \u0627\u0644\u062a\u0639\u0645\u0642 \u0641\u064a \u0627\u0644\u0645\u0646\u0637\u0642 \u0627\u0644\u0642\u0636\u0627\u064a\u0627 \u0648\u062a\u0637\u0648\u064a\u0631 \u0645\u0647\u0627\u0631\u0627\u062a\u0643 \u0641\u064a \u0625\u062b\u0628\u0627\u062a \u0627\u0644\u0646\u0638\u0631\u064a\u0627\u062a\u060c \u0641\u0633\u062a\u0643\u0648\u0646 \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629 \u0645\u0641\u064a\u062f\u0629 \u0644\u0644\u063a\u0627\u064a\u0629.<\/em><\/p>\n<p><\/center><br \/>\n<\/p>\n<p><strong>\u0623\u0647\u062f\u0627\u0641 \u0627\u0644\u062a\u0639\u0644\u0645:<\/strong><\/p>\n<ol>\n<li><strong>\u0641\u0647\u0645<\/strong> \u0627\u0644\u0623\u0633\u0627\u0633 \u0648\u0631\u0627\u0621 \u062a\u0642\u0646\u064a\u0627\u062a \u0625\u062f\u062e\u0627\u0644 \u0648\u0625\u0632\u0627\u0644\u0629 \u0627\u0644\u0627\u0642\u062a\u0631\u0627\u0646\u0627\u062a \u0648\u0627\u0644\u0627\u0646\u0641\u0635\u0627\u0644\u0627\u062a.<\/li>\n<li><strong>\u0641\u0647\u0645<\/strong> \u062e\u0627\u0635\u064a\u0629 \u0627\u0644\u062b\u0627\u0644\u062b \u0627\u0644\u0645\u0633\u062a\u0628\u0639\u062f \u0623\u0648 \u0627\u0644\u0628\u062f\u064a\u0647\u064a\u0629 (TAU) \u0641\u064a \u0627\u0644\u0645\u0646\u0637\u0642 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a.<\/li>\n<li><strong>\u0641\u0647\u0645<\/strong> \u0642\u0627\u0646\u0648\u0646 \u0627\u0644\u062a\u0646\u0627\u0642\u0636 (CON) \u0623\u0648 \u0645\u0628\u062f\u0623 \u0627\u0644\u0627\u0646\u0641\u062c\u0627\u0631 \u0641\u064a \u0627\u0644\u0645\u0646\u0637\u0642 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a.<\/li>\n<li><strong>\u0641\u0647\u0645<\/strong> \u062a\u0642\u0646\u064a\u0629 \u0625\u0632\u0627\u0644\u0629 \u0627\u0644\u0627\u0646\u0641\u0635\u0627\u0644\u0627\u062a (\u2228-\u0625\u0632\u0627\u0644\u0629) \u0641\u064a \u0627\u0644\u0645\u0646\u0637\u0642 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a.<\/li>\n<li><strong>\u0641\u0647\u0645<\/strong> \u062a\u0642\u0646\u064a\u0629 \u0627\u0644\u0625\u062b\u0628\u0627\u062a \u0628\u0627\u0644\u062d\u0627\u0644\u0627\u062a (CAS) \u0641\u064a \u0627\u0644\u0645\u0646\u0637\u0642 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a.<\/li>\n<li><strong>\u0641\u0647\u0645<\/strong> \u062a\u0642\u0646\u064a\u0629 \u0627\u0644\u062a\u0642\u0644\u064a\u0644 \u0625\u0644\u0649 \u0627\u0644\u0639\u0628\u062b (absurdo) \u0641\u064a \u0627\u0644\u0645\u0646\u0637\u0642 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a.<\/li>\n<li><strong>\u062a\u0637\u0628\u064a\u0642<\/strong> \u0645\u0639\u0631\u0641\u0629 \u0627\u0644\u062a\u0642\u0646\u064a\u0627\u062a \u0627\u0644\u0645\u062e\u062a\u0644\u0641\u0629 \u0644\u0644\u0645\u0646\u0637\u0642 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a \u0644\u062d\u0644 \u0627\u0644\u0645\u0634\u0643\u0644\u0627\u062a \u0648\u0627\u0644\u0628\u0631\u0627\u0647\u064a\u0646 \u0627\u0644\u0645\u0639\u0642\u062f\u0629.<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><strong>\u0627\u0644\u0641\u0647\u0631\u0633<\/strong><br \/>\n<a href=\"#1\"><strong>\u0625\u062f\u062e\u0627\u0644 \u0648\u0625\u0632\u0627\u0644\u0629 \u0627\u0644\u0627\u0642\u062a\u0631\u0627\u0646\u0627\u062a \u0648\u0627\u0644\u0627\u0646\u0641\u0635\u0627\u0644\u0627\u062a<\/strong><\/a><br \/>\n<a href=\"#2\">\u2228-\u0627\u0644\u0625\u062f\u062e\u0627\u0644<\/a><br \/>\n<a href=\"#3\">\u2228-\u0627\u0644\u0625\u0632\u0627\u0644\u0629<\/a><br \/>\n<a href=\"#4\">\u2227-\u0627\u0644\u0625\u062f\u062e\u0627\u0644<\/a><br \/>\n<a href=\"#5\">\u2227-\u0627\u0644\u0625\u0632\u0627\u0644\u0629<\/a><br \/>\n<a href=\"#6\"><strong>\u062a\u0642\u0646\u064a\u0627\u062a \u0627\u0644\u062a\u0646\u0627\u0642\u0636 \u0648\u0627\u0644\u0628\u062f\u064a\u0647\u064a\u0627\u062a<\/strong><\/a><br \/>\n<a href=\"#7\">\u0642\u0627\u0646\u0648\u0646 \u0627\u0644\u062b\u0627\u0644\u062b \u0627\u0644\u0645\u0633\u062a\u0628\u0639\u062f \u0623\u0648 \u0627\u0644\u0628\u062f\u064a\u0647\u064a\u0629 (TAU)<\/a><br \/>\n<a href=\"#8\">\u0642\u0627\u0646\u0648\u0646 \u0627\u0644\u062a\u0646\u0627\u0642\u0636 \u0623\u0648 \u0645\u0628\u062f\u0623 \u0627\u0644\u0627\u0646\u0641\u062c\u0627\u0631<\/a><br \/>\n<a href=\"#9\">\u2228-\u0627\u0644\u0625\u0632\u0627\u0644\u06293<\/a><br \/>\n<a href=\"#10\">\u0627\u0644\u0625\u062b\u0628\u0627\u062a \u0628\u0627\u0644\u062d\u0627\u0644\u0627\u062a (CAS)<\/a><br \/>\n<a href=\"#11\">\u0627\u0644\u062a\u0642\u0644\u064a\u0644 \u0625\u0644\u0649 \u0627\u0644\u0639\u0628\u062b (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>\u0625\u062f\u062e\u0627\u0644 \u0648\u0625\u0632\u0627\u0644\u0629 \u0627\u0644\u0627\u0642\u062a\u0631\u0627\u0646\u0627\u062a \u0648\u0627\u0644\u0627\u0646\u0641\u0635\u0627\u0644\u0627\u062a<\/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;\">\u0623\u062d\u062f \u062a\u0642\u0646\u064a\u0627\u062a<\/span><\/strong><\/a> \u0627\u0644\u0645\u0646\u0637\u0642 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a \u0647\u064a \u0625\u062f\u062e\u0627\u0644 \u0648\u0625\u0632\u0627\u0644\u0629 \u0627\u0644\u0648\u0635\u0644\u0627\u062a \u0648\u0627\u0644\u0641\u0635\u0644\u0627\u062a. \u0639\u0644\u0649 \u0627\u0644\u0631\u063a\u0645 \u0645\u0646 \u0623\u0646 \u0647\u0630\u0647 \u0627\u0644\u062a\u0642\u0646\u064a\u0627\u062a \u064a\u062a\u0645 \u062a\u0646\u0641\u064a\u0630\u0647\u0627 \u0628\u0637\u0631\u064a\u0642\u0629 \u0623\u0643\u062b\u0631 \u0623\u0648 \u0623\u0642\u0644 \u0628\u062f\u064a\u0647\u064a\u0629\u060c \u0641\u0625\u0646 \u062a\u0628\u0631\u064a\u0631\u0647\u0627 \u0644\u064a\u0633 \u062a\u0627\u0641\u0647\u064b\u0627 \u062a\u0645\u0627\u0645\u064b\u0627\u060c \u0648\u0644\u0643\u0646 \u064a\u0645\u0643\u0646 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u064a\u0647\u0627 \u0645\u0646 \u0642\u0648\u0627\u0639\u062f \u0627\u0644\u0645\u0646\u0637\u0642 \u0627\u0644\u0642\u0636\u0627\u064a\u0627 \u0627\u0644\u062a\u064a \u0623\u062b\u0628\u062a\u0646\u0627\u0647\u0627 \u0628\u0627\u0644\u0641\u0639\u0644 \u0641\u064a \u0627\u0644\u062f\u0631\u0648\u0633 \u0627\u0644\u0633\u0627\u0628\u0642\u0629. \u0628\u0634\u0643\u0644 \u0631\u0633\u0645\u064a\u060c \u062a\u0642\u0646\u064a\u0627\u062a \u0625\u062f\u062e\u0627\u0644 \u0648\u0625\u0632\u0627\u0644\u0629 \u0627\u0644\u0648\u0635\u0644\u0627\u062a \u0648\u0627\u0644\u0641\u0635\u0644\u0627\u062a \u0647\u064a \u0643\u0645\u0627 \u064a\u0644\u064a:<\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td>\u2228-\u0627\u0644\u0625\u062f\u062e\u0627\u0644<\/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-\u0627\u0644\u0625\u0632\u0627\u0644\u0629<\/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-\u0627\u0644\u0625\u062f\u062e\u0627\u0644<\/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-\u0627\u0644\u0625\u0632\u0627\u0644\u0629<\/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;\">\u0648\u062f\u0644\u064a\u0644\u0647\u0627 \u0645\u0646 \u0627\u0644\u0645\u0646\u0637\u0642 \u0627\u0644\u0642\u0636\u0627\u064a\u0627 \u0647\u0648 \u0643\u0645\u0627 \u064a\u0644\u064a:<\/p>\n<p><a name=\"2\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h3>\u2228-\u0627\u0644\u0625\u062f\u062e\u0627\u0644<\/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>; \u0627\u0641\u062a\u0631\u0627\u0636<\/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, \u0623\u062d\u0627\u062f\u064a\u0629<\/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>-\u062a\u0639\u0631\u064a\u0641(3)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"3\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h3>\u2228-\u0627\u0644\u0625\u0632\u0627\u0644\u0629<\/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>; \u0627\u0641\u062a\u0631\u0627\u0636<\/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>; \u0627\u0641\u062a\u0631\u0627\u0636<\/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>-\u062a\u0639\u0631\u064a\u0641 (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-\u0627\u0644\u0625\u062f\u062e\u0627\u0644<\/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>-\u0625\u0632\u0627\u0644\u0629<\/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>; \u0623\u062d\u0627\u062f\u064a\u0629 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>; \u0627\u0641\u062a\u0631\u0627\u0636<\/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>; \u0627\u0641\u062a\u0631\u0627\u0636<\/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>-\u062a\u0639\u0631\u064a\u0641(11)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"5\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h3>\u2227-\u0627\u0644\u0625\u0632\u0627\u0644\u0629<\/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>; \u0627\u0641\u062a\u0631\u0627\u0636<\/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>-\u0627\u0644\u0625\u062f\u062e\u0627\u0644<\/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>-\u062a\u0639\u0631\u064a\u0641(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>; \u0623\u062d\u0627\u062f\u064a\u0629(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>\u062a\u0642\u0646\u064a\u0627\u062a \u0627\u0644\u062a\u0646\u0627\u0642\u0636 \u0648\u0627\u0644\u0628\u062f\u064a\u0647\u064a\u0627\u062a<\/h2>\n<p><a name=\"7\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h3>\u0642\u0627\u0646\u0648\u0646 \u0627\u0644\u062b\u0627\u0644\u062b \u0627\u0644\u0645\u0633\u062a\u0628\u0639\u062f \u0623\u0648 \u0627\u0644\u0628\u062f\u064a\u0647\u064a\u0629 (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;\">\u062e\u0627\u0635\u064a\u0629 \u0623\u062e\u0631\u0649 \u0628\u0627\u0631\u0632\u0629 \u0644\u0644\u0645\u0646\u0637\u0642 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a<\/span><\/strong><\/a> \u0647\u064a \u062e\u0627\u0635\u064a\u0629 \u0627\u0644\u062b\u0627\u0644\u062b \u0627\u0644\u0645\u0633\u062a\u0628\u0639\u062f (tertium non datur). \u064a\u0646\u0635 \u0639\u0644\u0649 \u0623\u0646\u0647 \u0625\u0630\u0627 \u0643\u0627\u0646 \u0647\u0646\u0627\u0643 \u0628\u064a\u0627\u0646\u062a\u0627\u0646\u060c \u062d\u064a\u062b \u064a\u0646\u0641\u064a \u0623\u062d\u062f\u0647\u0645\u0627 \u0627\u0644\u0622\u062e\u0631\u060c \u0641\u064a\u062c\u0628 \u0623\u0646 \u062a\u0643\u0648\u0646 \u0625\u062d\u062f\u0627\u0647\u0645\u0627 \u0635\u062d\u064a\u062d\u0629 \u0628\u0627\u0644\u0636\u0631\u0648\u0631\u0629\u061b \u0623\u0648 \u0628\u0639\u0628\u0627\u0631\u0629 \u0623\u062e\u0631\u0649\u060c \u0641\u0625\u0646 \u0627\u0642\u062a\u0631\u0627\u0646 \u0628\u064a\u0627\u0646\u064a\u0646 \u0623\u062d\u062f\u0647\u0645\u0627 \u064a\u0646\u0641\u064a \u0627\u0644\u0622\u062e\u0631 \u064a\u0634\u0643\u0644 \u0628\u0627\u0644\u0636\u0631\u0648\u0631\u0629 \u0628\u062f\u064a\u0647\u064a\u0629. \u0628\u0634\u0643\u0644 \u0631\u0633\u0645\u064a\u060c \u064a\u064f\u0639\u0628\u0631 \u0639\u0646 \u0630\u0644\u0643 \u0628\u0627\u0644\u0643\u062a\u0627\u0628\u0629:<\/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;\">\u0648\u062f\u0644\u064a\u0644\u0647\u0627 \u0633\u0647\u0644 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u064a\u0647.<\/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>; \u0627\u0641\u062a\u0631\u0627\u0636<\/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>; \u0645\u0646 (2) \u0644\u0623\u0646 <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;\">\u0637\u0631\u064a\u0642\u0629 \u0623\u062e\u0631\u0649 \u0644\u0625\u0639\u0644\u0627\u0646 \u0645\u0628\u062f\u0623 \u0627\u0644\u062b\u0627\u0644\u062b \u0627\u0644\u0645\u0633\u062a\u0628\u0639\u062f \u0647\u064a \u0639\u0628\u0631 \u0642\u0627\u0646\u0648\u0646 <strong>\u0639\u062f\u0645 \u0627\u0644\u062a\u0646\u0627\u0642\u0636<\/strong>\u060c \u0627\u0644\u0630\u064a \u064a\u0646\u0635 \u0639\u0644\u0649 \u0623\u0646 \u0627\u0644\u0628\u064a\u0627\u0646 \u0644\u0627 \u064a\u0645\u0643\u0646 \u0623\u0646 \u064a\u0643\u0648\u0646 \u0635\u062d\u064a\u062d\u064b\u0627 \u0648\u062e\u0627\u0637\u0626\u064b\u0627 \u0641\u064a \u0646\u0641\u0633 \u0627\u0644\u0648\u0642\u062a \u0648\u064a\u062a\u0645 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0639\u0646\u0647 \u0631\u0633\u0645\u064a\u064b\u0627 \u0639\u0628\u0631:<\/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;\">\u0647\u0630\u0647 \u0627\u0644\u062e\u0627\u0635\u064a\u0629 \u0644\u0627 \u062a\u062d\u062a\u0627\u062c \u0625\u0644\u0649 \u0625\u062b\u0628\u0627\u062a\u060c \u0644\u064a\u0633 \u0644\u0623\u0646\u0647\u0627 \u0628\u062f\u064a\u0647\u064a\u0629 \u0628\u062d\u062f \u0630\u0627\u062a\u0647\u0627\u060c \u0648\u0644\u0643\u0646 \u0644\u0623\u0646\u0647\u0627 \u062a\u064f\u0633\u062a\u0645\u062f \u0645\u0628\u0627\u0634\u0631\u0629 \u0645\u0646 \u062a\u0637\u0628\u064a\u0642 \u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0627\u0642\u062a\u0631\u0627\u0646 \u0639\u0644\u0649 \u0645\u0628\u062f\u0623 \u0627\u0644\u062b\u0627\u0644\u062b \u0627\u0644\u0645\u0633\u062a\u0628\u0639\u062f.<\/p>\n<p><a name=\"8\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h3>\u0642\u0627\u0646\u0648\u0646 \u0627\u0644\u062a\u0646\u0627\u0642\u0636 \u0623\u0648 \u0645\u0628\u062f\u0623 \u0627\u0644\u0627\u0646\u0641\u062c\u0627\u0631<\/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;\">\u062e\u0627\u0635\u064a\u0629 \u0623\u062e\u0631\u0649 \u0645\u0639\u0631\u0648\u0641\u0629 \u0644\u0644\u0645\u0646\u0637\u0642 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a<\/span><\/strong><\/a> \u0647\u064a \u0645\u0628\u062f\u0623 \u0627\u0644\u0627\u0646\u0641\u062c\u0627\u0631\u060c \u0627\u0644\u0630\u064a \u064a\u064f\u0639\u0644\u0646 \u0639\u0627\u062f\u0629 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u0639\u0628\u0627\u0631\u0629 \u00ab\u0645\u0646 \u0645\u0642\u062f\u0645\u0627\u062a \u0645\u062a\u0646\u0627\u0642\u0636\u0629 \u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u0646\u062a\u0627\u062c \u0623\u064a \u0634\u064a\u0621\u00bb. \u064a\u064f\u0639\u0631\u0636 \u0639\u0627\u062f\u0629 \u0628\u0635\u064a\u063a\u062a\u064a\u0646:<\/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;\">\u0648\u062f\u0644\u064a\u0644 \u0647\u0630\u0627 \u0627\u0644\u0642\u0627\u0646\u0648\u0646 \u0628\u0633\u064a\u0637:<\/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>; \u0627\u0641\u062a\u0631\u0627\u0636<\/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>-\u0627\u0644\u0625\u062f\u062e\u0627\u0644<\/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>-\u062a\u0639\u0631\u064a\u0641(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>; \u0627\u0641\u062a\u0631\u0627\u0636<\/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-\u0627\u0644\u0625\u0632\u0627\u0644\u06293<\/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;\">\u064a\u0645\u0643\u0646 \u0643\u062a\u0627\u0628\u0629 \u0642\u0648\u0627\u0639\u062f \u0627\u0644\u0645\u0646\u0637\u0642 \u0628\u0637\u0631\u064a\u0642\u062a\u064a\u0646 \u0645\u062e\u062a\u0644\u0641\u062a\u064a\u0646<\/span><\/strong><\/a>. \u0625\u062d\u062f\u0649 \u0627\u0644\u0635\u064a\u063a \u0627\u0644\u062a\u064a \u0646\u0639\u0631\u0641\u0647\u0627 \u0628\u0627\u0644\u0641\u0639\u0644 \u0647\u064a<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\alpha,(\\alpha \\rightarrow \\beta)\\}\\vdash \\beta<\/span><\/span>. \u0627\u0644\u0623\u062e\u0631\u0649 \u0623\u0642\u0644 \u0634\u0647\u0631\u0629:<\/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;\">\u0628\u062a\u0631\u0643\u064a\u0632\u0646\u0627 \u0639\u0644\u0649 \u0647\u0630\u0647 \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u062b\u0627\u0646\u064a\u0629\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u062a\u0635\u0648\u0631 \u062a\u0648\u0633\u0639 \u0644\u0647\u0630\u0647 \u0627\u0644\u0642\u0627\u0639\u062f\u0629 \u0646\u0633\u0645\u064a\u0647 <strong>\u2228-\u0627\u0644\u0625\u0632\u0627\u0644\u06293<\/strong>\u060c \u0644\u0623\u0646\u0647 \u064a\u0634\u0628\u0647 \u0627\u0644\u062a\u0628\u0633\u064a\u0637 \u0627\u0644\u0646\u0627\u062a\u062c \u0639\u0646 \u0627\u0646\u0641\u0635\u0627\u0644. \u0647\u0630\u0647 \u0627\u0644\u0642\u0627\u0639\u062f\u0629 \u062a\u0642\u0648\u0644 \u0625\u0646\u0647 \u0625\u0630\u0627 \u0643\u0627\u0646 \u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u0646\u062a\u0627\u062c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\gamma<\/span><\/span> \u0645\u0646<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span> \u0648<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\beta<\/span><\/span> (\u0643\u0644\u064a\u0647\u0645\u0627 \u0645\u0639\u064b\u0627) \u0648<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span> \u0648<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\beta<\/span><\/span> \u0628\u064a\u0646\u0647\u0645\u0627 \u0627\u0646\u0641\u0635\u0627\u0644\u060c \u0641\u0625\u0646<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\gamma<\/span><\/span> \u0647\u0648 \u0646\u0638\u0631\u064a\u0629. \u0647\u0630\u0627 \u064a\u0645\u0643\u0646 \u062a\u0644\u062e\u064a\u0635\u0647 \u0631\u0633\u0645\u064a\u064b\u0627 \u0643\u0645\u0627 \u064a\u0644\u064a:<\/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;\">\u0648\u062f\u0644\u064a\u0644 \u0647\u0630\u0647 \u0627\u0644\u062a\u0642\u0646\u064a\u0629 \u0645\u0646 \u0627\u0644\u0645\u0646\u0637\u0642 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a \u0647\u0648 \u0643\u0645\u0627 \u064a\u0644\u064a:<\/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>; \u0627\u0641\u062a\u0631\u0627\u0636<\/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>; \u0627\u0641\u062a\u0631\u0627\u0636<\/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>; \u0627\u0641\u062a\u0631\u0627\u0636<\/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>-\u0627\u0644\u0625\u062f\u062e\u0627\u0644(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; \u062a\u0639\u0631\u064a\u0641<\/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>; \u0646\u0641\u064a \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0646 \u0641\u064a (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>; \u0627\u0633\u062a\u0628\u062f\u0627\u0644 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">A:=\\neg\\alpha<\/span><\/span> \u0648 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">B:=\\neg\\beta<\/span><\/span> \u0641\u064a (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>\u0627\u0644\u0625\u062b\u0628\u0627\u062a \u0628\u0627\u0644\u062d\u0627\u0644\u0627\u062a (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;\">\u0625\u062d\u062f\u0649 \u062a\u0642\u0646\u064a\u0627\u062a \u0627\u0644\u0645\u0646\u0637\u0642 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a<\/span><\/a> \u0647\u064a \u0627\u0644\u0625\u062b\u0628\u0627\u062a \u0628\u0627\u0644\u062d\u0627\u0644\u0627\u062a. \u0625\u0630\u0627 \u0643\u0627\u0646 \u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u0646\u062a\u0627\u062c \u062a\u0639\u0628\u064a\u0631<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\beta<\/span><\/span> \u0645\u0646 \u062a\u0639\u0628\u064a\u0631 \u0622\u062e\u0631<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span> \u0648\u0645\u0646 \u0646\u0641\u064a\u0647\u060c \u0641\u0625\u0646 \u0627\u0644\u062a\u0639\u0628\u064a\u0631<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\beta<\/span><\/span> \u064a\u0643\u0648\u0646 \u0628\u0627\u0644\u0636\u0631\u0648\u0631\u0629 \u0646\u0638\u0631\u064a\u0629. \u064a\u062a\u0645 \u062a\u0645\u062b\u064a\u0644 \u0630\u0644\u0643 \u0628\u0634\u0643\u0644 \u0631\u0633\u0645\u064a \u0643\u0645\u0627 \u064a\u0644\u064a: <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>. \u0648\u062f\u0644\u064a\u0644\u0647\u0627 \u0647\u0648 \u0643\u0645\u0627 \u064a\u0644\u064a:<\/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;; \u0627\u0641\u062a\u0631\u0627\u0636\\\\\n\n(2) &amp; \\neg \\alpha \\vdash \\beta &amp;; \u0627\u0641\u062a\u0631\u0627\u0636 \\\\\n\n(3) &amp; \\vdash \\alpha \\vee \\neg\\alpha &amp;; TAU \\\\\n\n(4) &amp; \\vdash \\beta &amp;; \\vee-\u0625\u0632\u0627\u0644\u06293(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>\u0627\u0644\u062a\u0642\u0644\u064a\u0644 \u0625\u0644\u0649 \u0627\u0644\u0639\u0628\u062b (absurdo)<\/h3>\n<p style=\"text-align: justify; color: #000000;\">\u0623\u062d\u062f \u0623\u0643\u062b\u0631 \u062a\u0642\u0646\u064a\u0627\u062a \u0627\u0644\u0645\u0646\u0637\u0642 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a \u0627\u0633\u062a\u062e\u062f\u0627\u0645\u064b\u0627 \u0641\u064a \u0627\u0644\u0628\u0631\u0627\u0647\u064a\u0646\u060c \u062e\u0627\u0635\u0629 \u0641\u064a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a\u060c \u0647\u064a \u062a\u0642\u0646\u064a\u0629 \u0627\u0644\u062a\u0642\u0644\u064a\u0644 \u0625\u0644\u0649 \u0627\u0644\u0639\u0628\u062b. \u0647\u0630\u0627 \u064a\u0639\u0646\u064a \u0623\u0646\u0647 \u0625\u0630\u0627 \u062a\u0645 \u0627\u0633\u062a\u0646\u062a\u0627\u062c \u062a\u0646\u0627\u0642\u0636 (\u062a\u0639\u0628\u064a\u0631 \u0648\u0646\u0641\u064a\u0647) \u0645\u0646 \u062a\u0639\u0628\u064a\u0631<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span>\u060c \u0641\u0625\u0646 \u0646\u0641\u064a<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span> \u064a\u0643\u0648\u0646 \u0628\u062f\u064a\u0647\u064a\u0629. \u064a\u062a\u0645 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0639\u0646 \u0630\u0644\u0643 \u0628\u0634\u0643\u0644 \u0631\u0633\u0645\u064a \u0643\u0645\u0627 \u064a\u0644\u064a: <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>. \u0648\u062f\u0644\u064a\u0644\u0647\u0627 \u0647\u0648 \u0643\u0645\u0627 \u064a\u0644\u064a:<\/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>; \u0627\u0641\u062a\u0631\u0627\u0636<\/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>; \u0627\u0641\u062a\u0631\u0627\u0636<\/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>\u0639\u0631\u0636 \u062a\u0642\u0646\u064a\u0627\u062a \u0627\u0644\u0645\u0646\u0637\u0642 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a \u0645\u0644\u062e\u0635\u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629\u060c \u0646\u0642\u062f\u0645 \u0639\u062f\u0629 \u062a\u0642\u0646\u064a\u0627\u062a \u0644\u0644\u0645\u0646\u0637\u0642 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a \u0644\u0625\u062f\u062e\u0627\u0644 \u0648\u0625\u0632\u0627\u0644\u0629 \u0627\u0644\u0627\u0642\u062a\u0631\u0627\u0646\u0627\u062a \u0648\u0627\u0644\u0627\u0646\u0641\u0635\u0627\u0644\u0627\u062a\u060c \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0642\u0627\u0646\u0648\u0646 \u0627\u0644\u062b\u0627\u0644\u062b \u0627\u0644\u0645\u0633\u062a\u0628\u0639\u062f \u0648\u0642\u0627\u0646\u0648\u0646 \u0627\u0644\u062a\u0646\u0627\u0642\u0636\u060c \u0627\u0644\u0645\u0639\u0631\u0648\u0641 \u0623\u064a\u0636\u064b\u0627 \u0628\u0645\u0628\u062f\u0623 \u0627\u0644\u0627\u0646\u0641\u062c\u0627\u0631. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0646\u0634\u0631\u062d \u062a\u0642\u0646\u064a\u0629 \u0627\u0644\u0625\u062b\u0628\u0627\u062a \u0628\u0627\u0644\u062d\u0627\u0644\u0627\u062a \u0648\u062a\u0642\u0646\u064a\u0629 \u0627\u0644\u062a\u0642\u0644\u064a\u0644 \u0625\u0644\u0649 \u0627\u0644\u0639\u0628\u062b\u060c \u0648\u0643\u0644\u0627\u0647\u0645\u0627 \u0645\u0641\u064a\u062f \u062c\u062f\u064b\u0627 \u0641\u064a \u0627\u0644\u0628\u0631\u0627\u0647\u064a\u0646 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u0648\u0627\u0644\u0645\u0646\u0637\u0642\u064a\u0629 \u0628\u0634\u0643\u0644 \u0639\u0627\u0645. \u064a\u062a\u0645 \u062a\u0642\u062f\u064a\u0645 \u0643\u0644 \u062a\u0642\u0646\u064a\u0629 \u0628\u0634\u0643\u0644 \u0631\u0633\u0645\u064a \u0648\u064a\u062a\u0645 \u062a\u0648\u0641\u064a\u0631 [&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":2,"footnotes":""},"categories":[625,611,565],"tags":[],"class_list":["post-27468","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-625","category-611","category-565"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u0639\u0631\u0636 \u062a\u0642\u0646\u064a\u0627\u062a \u0627\u0644\u0645\u0646\u0637\u0642 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u0627\u0644\u0645\u0646\u0637\u0642 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a: \u0625\u062f\u062e\u0627\u0644 \u0648\u0625\u0632\u0627\u0644\u0629 \u0627\u0644\u0627\u0642\u062a\u0631\u0627\u0646\u0627\u062a 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