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Theorem List for Intuitionistic Logic Explorer - 1101-1200   *Has distinct variable group(s)
TypeLabelDescription
Statement
 
Theorem3impib 1101 Importation to triple conjunction. (Contributed by NM, 13-Jun-2006.)
   =>   
 
Theorem3exp 1102 Exportation inference. (Contributed by NM, 30-May-1994.)
   =>   
 
Theorem3expa 1103 Exportation from triple to double conjunction. (Contributed by NM, 20-Aug-1995.)
   =>   
 
Theorem3expb 1104 Exportation from triple to double conjunction. (Contributed by NM, 20-Aug-1995.)
   =>   
 
Theorem3expia 1105 Exportation from triple conjunction. (Contributed by NM, 19-May-2007.)
   =>   
 
Theorem3expib 1106 Exportation from triple conjunction. (Contributed by NM, 19-May-2007.)
   =>   
 
Theorem3com12 1107 Commutation in antecedent. Swap 1st and 3rd. (Contributed by NM, 28-Jan-1996.) (Proof shortened by Andrew Salmon, 13-May-2011.)
   =>   
 
Theorem3com13 1108 Commutation in antecedent. Swap 1st and 3rd. (Contributed by NM, 28-Jan-1996.)
   =>   
 
Theorem3com23 1109 Commutation in antecedent. Swap 2nd and 3rd. (Contributed by NM, 28-Jan-1996.)
   =>   
 
Theorem3coml 1110 Commutation in antecedent. Rotate left. (Contributed by NM, 28-Jan-1996.)
   =>   
 
Theorem3comr 1111 Commutation in antecedent. Rotate right. (Contributed by NM, 28-Jan-1996.)
   =>   
 
Theorem3adant3r1 1112 Deduction adding a conjunct to antecedent. (Contributed by NM, 16-Feb-2008.)
   =>   
 
Theorem3adant3r2 1113 Deduction adding a conjunct to antecedent. (Contributed by NM, 17-Feb-2008.)
   =>   
 
Theorem3adant3r3 1114 Deduction adding a conjunct to antecedent. (Contributed by NM, 18-Feb-2008.)
   =>   
 
Theorem3an1rs 1115 Swap conjuncts. (Contributed by NM, 16-Dec-2007.)
   =>   
 
Theorem3imp1 1116 Importation to left triple conjunction. (Contributed by NM, 24-Feb-2005.)
   =>   
 
Theorem3impd 1117 Importation deduction for triple conjunction. (Contributed by NM, 26-Oct-2006.)
   =>   
 
Theorem3imp2 1118 Importation to right triple conjunction. (Contributed by NM, 26-Oct-2006.)
   =>   
 
Theorem3exp1 1119 Exportation from left triple conjunction. (Contributed by NM, 24-Feb-2005.)
   =>   
 
Theorem3expd 1120 Exportation deduction for triple conjunction. (Contributed by NM, 26-Oct-2006.)
   =>   
 
Theorem3exp2 1121 Exportation from right triple conjunction. (Contributed by NM, 26-Oct-2006.)
   =>   
 
Theoremexp5o 1122 A triple exportation inference. (Contributed by Jeff Hankins, 8-Jul-2009.)
   =>   
 
Theoremexp516 1123 A triple exportation inference. (Contributed by Jeff Hankins, 8-Jul-2009.)
   =>   
 
Theoremexp520 1124 A triple exportation inference. (Contributed by Jeff Hankins, 8-Jul-2009.)
   =>   
 
Theorem3anassrs 1125 Associative law for conjunction applied to antecedent (eliminates syllogism). (Contributed by Mario Carneiro, 4-Jan-2017.)
   =>   
 
Theorem3adant1l 1126 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)
   =>   
 
Theorem3adant1r 1127 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)
   =>   
 
Theorem3adant2l 1128 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)
   =>   
 
Theorem3adant2r 1129 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)
   =>   
 
Theorem3adant3l 1130 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)
   =>   
 
Theorem3adant3r 1131 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)
   =>   
 
Theoremsyl12anc 1132 Syllogism combined with contraction. (Contributed by Jeff Hankins, 1-Aug-2009.)
   &       &       &       =>   
 
Theoremsyl21anc 1133 Syllogism combined with contraction. (Contributed by Jeff Hankins, 1-Aug-2009.)
   &       &       &       =>   
 
Theoremsyl3anc 1134 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
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Theoremsyl22anc 1135 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
   &       &       &       &       =>   
 
Theoremsyl13anc 1136 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
   &       &       &       &       =>   
 
Theoremsyl31anc 1137 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
   &       &       &       &       =>   
 
Theoremsyl112anc 1138 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
   &       &       &       &       =>   
 
Theoremsyl121anc 1139 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
   &       &       &       &       =>   
 
Theoremsyl211anc 1140 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
   &       &       &       &       =>   
 
Theoremsyl23anc 1141 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
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Theoremsyl32anc 1142 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
   &       &       &       &       &       =>   
 
Theoremsyl122anc 1143 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
   &       &       &       &       &       =>   
 
Theoremsyl212anc 1144 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
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Theoremsyl221anc 1145 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
   &       &       &       &       &       =>   
 
Theoremsyl113anc 1146 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
   &       &       &       &       &       =>   
 
Theoremsyl131anc 1147 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
   &       &       &       &       &       =>   
 
Theoremsyl311anc 1148 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
   &       &       &       &       &       =>   
 
Theoremsyl33anc 1149 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
   &       &       &       &       &       &       =>   
 
Theoremsyl222anc 1150 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
   &       &       &       &       &       &       =>   
 
Theoremsyl123anc 1151 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
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Theoremsyl132anc 1152 Syllogism combined with contraction. (Contributed by NM, 11-Jul-2012.)
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Theoremsyl213anc 1153 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
   &       &       &       &       &       &       =>   
 
Theoremsyl231anc 1154 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
   &       &       &       &       &       &       =>   
 
Theoremsyl312anc 1155 Syllogism combined with contraction. (Contributed by NM, 11-Jul-2012.)
   &       &       &       &       &       &       =>   
 
Theoremsyl321anc 1156 Syllogism combined with contraction. (Contributed by NM, 11-Jul-2012.)
   &       &       &       &       &       &       =>   
 
Theoremsyl133anc 1157 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
   &       &       &       &       &       &       &       =>   
 
Theoremsyl313anc 1158 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
   &       &       &       &       &       &       &       =>   
 
Theoremsyl331anc 1159 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
   &       &       &       &       &       &       &       =>   
 
Theoremsyl223anc 1160 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
   &       &       &       &       &       &       &       =>   
 
Theoremsyl232anc 1161 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
   &       &       &       &       &       &       &       =>   
 
Theoremsyl322anc 1162 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
   &       &       &       &       &       &       &       =>   
 
Theoremsyl233anc 1163 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
   &       &       &       &       &       &       &       &       =>   
 
Theoremsyl323anc 1164 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
   &       &       &       &       &       &       &       &       =>   
 
Theoremsyl332anc 1165 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
   &       &       &       &       &       &       &       &       =>   
 
Theoremsyl333anc 1166 A syllogism inference combined with contraction. (Contributed by NM, 10-Mar-2012.)
   &       &       &       &       &       &       &       &       &       =>   
 
Theoremsyl3an1 1167 A syllogism inference. (Contributed by NM, 22-Aug-1995.)
   &       =>   
 
Theoremsyl3an2 1168 A syllogism inference. (Contributed by NM, 22-Aug-1995.)
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Theoremsyl3an3 1169 A syllogism inference. (Contributed by NM, 22-Aug-1995.)
   &       =>   
 
Theoremsyl3an1b 1170 A syllogism inference. (Contributed by NM, 22-Aug-1995.)
   &       =>   
 
Theoremsyl3an2b 1171 A syllogism inference. (Contributed by NM, 22-Aug-1995.)
   &       =>   
 
Theoremsyl3an3b 1172 A syllogism inference. (Contributed by NM, 22-Aug-1995.)
   &       =>   
 
Theoremsyl3an1br 1173 A syllogism inference. (Contributed by NM, 22-Aug-1995.)
   &       =>   
 
Theoremsyl3an2br 1174 A syllogism inference. (Contributed by NM, 22-Aug-1995.)
   &       =>   
 
Theoremsyl3an3br 1175 A syllogism inference. (Contributed by NM, 22-Aug-1995.)
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Theoremsyl3an 1176 A triple syllogism inference. (Contributed by NM, 13-May-2004.)
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Theoremsyl3anb 1177 A triple syllogism inference. (Contributed by NM, 15-Oct-2005.)
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Theoremsyl3anbr 1178 A triple syllogism inference. (Contributed by NM, 29-Dec-2011.)
   &       &       &       =>   
 
Theoremsyld3an3 1179 A syllogism inference. (Contributed by NM, 20-May-2007.)
   &       =>   
 
Theoremsyld3an1 1180 A syllogism inference. (Contributed by NM, 7-Jul-2008.)
   &       =>   
 
Theoremsyld3an2 1181 A syllogism inference. (Contributed by NM, 20-May-2007.)
   &       =>   
 
Theoremsyl3anl1 1182 A syllogism inference. (Contributed by NM, 24-Feb-2005.)
   &       =>   
 
Theoremsyl3anl2 1183 A syllogism inference. (Contributed by NM, 24-Feb-2005.)
   &       =>   
 
Theoremsyl3anl3 1184 A syllogism inference. (Contributed by NM, 24-Feb-2005.)
   &       =>   
 
Theoremsyl3anl 1185 A triple syllogism inference. (Contributed by NM, 24-Dec-2006.)
   &       &       &       =>   
 
Theoremsyl3anr1 1186 A syllogism inference. (Contributed by NM, 31-Jul-2007.)
   &       =>   
 
Theoremsyl3anr2 1187 A syllogism inference. (Contributed by NM, 1-Aug-2007.)
   &       =>   
 
Theoremsyl3anr3 1188 A syllogism inference. (Contributed by NM, 23-Aug-2007.)
   &       =>   
 
Theorem3impdi 1189 Importation inference (undistribute conjunction). (Contributed by NM, 14-Aug-1995.)
   =>   
 
Theorem3impdir 1190 Importation inference (undistribute conjunction). (Contributed by NM, 20-Aug-1995.)
   =>   
 
Theorem3anidm12 1191 Inference from idempotent law for conjunction. (Contributed by NM, 7-Mar-2008.)
   =>   
 
Theorem3anidm13 1192 Inference from idempotent law for conjunction. (Contributed by NM, 7-Mar-2008.)
   =>   
 
Theorem3anidm23 1193 Inference from idempotent law for conjunction. (Contributed by NM, 1-Feb-2007.)
   =>   
 
Theorem3ori 1194 Infer implication from triple disjunction. (Contributed by NM, 26-Sep-2006.)
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Theorem3jao 1195 Disjunction of 3 antecedents. (Contributed by NM, 8-Apr-1994.)
 
Theorem3jaob 1196 Disjunction of 3 antecedents. (Contributed by NM, 13-Sep-2011.)
 
Theorem3jaoi 1197 Disjunction of 3 antecedents (inference). (Contributed by NM, 12-Sep-1995.)
   &       &       =>   
 
Theorem3jaod 1198 Disjunction of 3 antecedents (deduction). (Contributed by NM, 14-Oct-2005.)
   &       &       =>   
 
Theorem3jaoian 1199 Disjunction of 3 antecedents (inference). (Contributed by NM, 14-Oct-2005.)
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Theorem3jaodan 1200 Disjunction of 3 antecedents (deduction). (Contributed by NM, 14-Oct-2005.)
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