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Theorem List for Intuitionistic Logic Explorer - 1101-1200   *Has distinct variable group(s)
TypeLabelDescription
Statement

Theorem3impia 1101 Importation to triple conjunction. (Contributed by NM, 13-Jun-2006.)

Theorem3impib 1102 Importation to triple conjunction. (Contributed by NM, 13-Jun-2006.)

Theorem3exp 1103 Exportation inference. (Contributed by NM, 30-May-1994.)

Theorem3expa 1104 Exportation from triple to double conjunction. (Contributed by NM, 20-Aug-1995.)

Theorem3expb 1105 Exportation from triple to double conjunction. (Contributed by NM, 20-Aug-1995.)

Theorem3expia 1106 Exportation from triple conjunction. (Contributed by NM, 19-May-2007.)

Theorem3expib 1107 Exportation from triple conjunction. (Contributed by NM, 19-May-2007.)

Theorem3com12 1108 Commutation in antecedent. Swap 1st and 3rd. (Contributed by NM, 28-Jan-1996.) (Proof shortened by Andrew Salmon, 13-May-2011.)

Theorem3com13 1109 Commutation in antecedent. Swap 1st and 3rd. (Contributed by NM, 28-Jan-1996.)

Theorem3com23 1110 Commutation in antecedent. Swap 2nd and 3rd. (Contributed by NM, 28-Jan-1996.)

Theorem3coml 1111 Commutation in antecedent. Rotate left. (Contributed by NM, 28-Jan-1996.)

Theorem3comr 1112 Commutation in antecedent. Rotate right. (Contributed by NM, 28-Jan-1996.)

Theorem3adant3r1 1113 Deduction adding a conjunct to antecedent. (Contributed by NM, 16-Feb-2008.)

Theorem3adant3r2 1114 Deduction adding a conjunct to antecedent. (Contributed by NM, 17-Feb-2008.)

Theorem3adant3r3 1115 Deduction adding a conjunct to antecedent. (Contributed by NM, 18-Feb-2008.)

Theorem3an1rs 1116 Swap conjuncts. (Contributed by NM, 16-Dec-2007.)

Theorem3imp1 1117 Importation to left triple conjunction. (Contributed by NM, 24-Feb-2005.)

Theorem3impd 1118 Importation deduction for triple conjunction. (Contributed by NM, 26-Oct-2006.)

Theorem3imp2 1119 Importation to right triple conjunction. (Contributed by NM, 26-Oct-2006.)

Theorem3exp1 1120 Exportation from left triple conjunction. (Contributed by NM, 24-Feb-2005.)

Theorem3expd 1121 Exportation deduction for triple conjunction. (Contributed by NM, 26-Oct-2006.)

Theorem3exp2 1122 Exportation from right triple conjunction. (Contributed by NM, 26-Oct-2006.)

Theoremexp5o 1123 A triple exportation inference. (Contributed by Jeff Hankins, 8-Jul-2009.)

Theoremexp516 1124 A triple exportation inference. (Contributed by Jeff Hankins, 8-Jul-2009.)

Theoremexp520 1125 A triple exportation inference. (Contributed by Jeff Hankins, 8-Jul-2009.)

Theorem3anassrs 1126 Associative law for conjunction applied to antecedent (eliminates syllogism). (Contributed by Mario Carneiro, 4-Jan-2017.)

Theorem3adant1l 1127 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)

Theorem3adant1r 1128 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)

Theorem3adant2l 1129 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)

Theorem3adant2r 1130 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)

Theorem3adant3l 1131 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)

Theorem3adant3r 1132 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)

Theoremsyl12anc 1133 Syllogism combined with contraction. (Contributed by Jeff Hankins, 1-Aug-2009.)

Theoremsyl21anc 1134 Syllogism combined with contraction. (Contributed by Jeff Hankins, 1-Aug-2009.)

Theoremsyl3anc 1135 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl22anc 1136 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl13anc 1137 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl31anc 1138 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl112anc 1139 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl121anc 1140 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl211anc 1141 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl23anc 1142 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl32anc 1143 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl122anc 1144 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl212anc 1145 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl221anc 1146 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl113anc 1147 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl131anc 1148 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl311anc 1149 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl33anc 1150 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl222anc 1151 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl123anc 1152 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl132anc 1153 Syllogism combined with contraction. (Contributed by NM, 11-Jul-2012.)

Theoremsyl213anc 1154 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl231anc 1155 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl312anc 1156 Syllogism combined with contraction. (Contributed by NM, 11-Jul-2012.)

Theoremsyl321anc 1157 Syllogism combined with contraction. (Contributed by NM, 11-Jul-2012.)

Theoremsyl133anc 1158 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl313anc 1159 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl331anc 1160 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl223anc 1161 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl232anc 1162 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl322anc 1163 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl233anc 1164 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl323anc 1165 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl332anc 1166 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl333anc 1167 A syllogism inference combined with contraction. (Contributed by NM, 10-Mar-2012.)

Theoremsyl3an1 1168 A syllogism inference. (Contributed by NM, 22-Aug-1995.)

Theoremsyl3an2 1169 A syllogism inference. (Contributed by NM, 22-Aug-1995.)

Theoremsyl3an3 1170 A syllogism inference. (Contributed by NM, 22-Aug-1995.)

Theoremsyl3an1b 1171 A syllogism inference. (Contributed by NM, 22-Aug-1995.)

Theoremsyl3an2b 1172 A syllogism inference. (Contributed by NM, 22-Aug-1995.)

Theoremsyl3an3b 1173 A syllogism inference. (Contributed by NM, 22-Aug-1995.)

Theoremsyl3an1br 1174 A syllogism inference. (Contributed by NM, 22-Aug-1995.)

Theoremsyl3an2br 1175 A syllogism inference. (Contributed by NM, 22-Aug-1995.)

Theoremsyl3an3br 1176 A syllogism inference. (Contributed by NM, 22-Aug-1995.)

Theoremsyl3an 1177 A triple syllogism inference. (Contributed by NM, 13-May-2004.)

Theoremsyl3anb 1178 A triple syllogism inference. (Contributed by NM, 15-Oct-2005.)

Theoremsyl3anbr 1179 A triple syllogism inference. (Contributed by NM, 29-Dec-2011.)

Theoremsyld3an3 1180 A syllogism inference. (Contributed by NM, 20-May-2007.)

Theoremsyld3an1 1181 A syllogism inference. (Contributed by NM, 7-Jul-2008.)

Theoremsyld3an2 1182 A syllogism inference. (Contributed by NM, 20-May-2007.)

Theoremsyl3anl1 1183 A syllogism inference. (Contributed by NM, 24-Feb-2005.)

Theoremsyl3anl2 1184 A syllogism inference. (Contributed by NM, 24-Feb-2005.)

Theoremsyl3anl3 1185 A syllogism inference. (Contributed by NM, 24-Feb-2005.)

Theoremsyl3anl 1186 A triple syllogism inference. (Contributed by NM, 24-Dec-2006.)

Theoremsyl3anr1 1187 A syllogism inference. (Contributed by NM, 31-Jul-2007.)

Theoremsyl3anr2 1188 A syllogism inference. (Contributed by NM, 1-Aug-2007.)

Theoremsyl3anr3 1189 A syllogism inference. (Contributed by NM, 23-Aug-2007.)

Theorem3impdi 1190 Importation inference (undistribute conjunction). (Contributed by NM, 14-Aug-1995.)

Theorem3impdir 1191 Importation inference (undistribute conjunction). (Contributed by NM, 20-Aug-1995.)

Theorem3anidm12 1192 Inference from idempotent law for conjunction. (Contributed by NM, 7-Mar-2008.)

Theorem3anidm13 1193 Inference from idempotent law for conjunction. (Contributed by NM, 7-Mar-2008.)

Theorem3anidm23 1194 Inference from idempotent law for conjunction. (Contributed by NM, 1-Feb-2007.)

Theorem3ori 1195 Infer implication from triple disjunction. (Contributed by NM, 26-Sep-2006.)

Theorem3jao 1196 Disjunction of 3 antecedents. (Contributed by NM, 8-Apr-1994.)

Theorem3jaob 1197 Disjunction of 3 antecedents. (Contributed by NM, 13-Sep-2011.)

Theorem3jaoi 1198 Disjunction of 3 antecedents (inference). (Contributed by NM, 12-Sep-1995.)

Theorem3jaod 1199 Disjunction of 3 antecedents (deduction). (Contributed by NM, 14-Oct-2005.)

Theorem3jaoian 1200 Disjunction of 3 antecedents (inference). (Contributed by NM, 14-Oct-2005.)

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