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

Theorem3anim1i 1101 Add two conjuncts to antecedent and consequent. (Contributed by Jeff Hankins, 16-Aug-2009.)

Theorem3anim2i 1102 Add two conjuncts to antecedent and consequent. (Contributed by AV, 21-Nov-2019.)

Theorem3anim3i 1103 Add two conjuncts to antecedent and consequent. (Contributed by Jeff Hankins, 19-Aug-2009.)

Theorem3anbi123i 1104 Join 3 biconditionals with conjunction. (Contributed by NM, 21-Apr-1994.)

Theorem3orbi123i 1105 Join 3 biconditionals with disjunction. (Contributed by NM, 17-May-1994.)

Theorem3anbi1i 1106 Inference adding two conjuncts to each side of a biconditional. (Contributed by NM, 8-Sep-2006.)

Theorem3anbi2i 1107 Inference adding two conjuncts to each side of a biconditional. (Contributed by NM, 8-Sep-2006.)

Theorem3anbi3i 1108 Inference adding two conjuncts to each side of a biconditional. (Contributed by NM, 8-Sep-2006.)

Theorem3imp 1109 Importation inference. (Contributed by NM, 8-Apr-1994.)

Theorem3impa 1110 Importation from double to triple conjunction. (Contributed by NM, 20-Aug-1995.)

Theorem3impb 1111 Importation from double to triple conjunction. (Contributed by NM, 20-Aug-1995.)

Theorem3impia 1112 Importation to triple conjunction. (Contributed by NM, 13-Jun-2006.)

Theorem3impib 1113 Importation to triple conjunction. (Contributed by NM, 13-Jun-2006.)

Theorem3exp 1114 Exportation inference. (Contributed by NM, 30-May-1994.)

Theorem3expa 1115 Exportation from triple to double conjunction. (Contributed by NM, 20-Aug-1995.)

Theorem3expb 1116 Exportation from triple to double conjunction. (Contributed by NM, 20-Aug-1995.)

Theorem3expia 1117 Exportation from triple conjunction. (Contributed by NM, 19-May-2007.)

Theorem3expib 1118 Exportation from triple conjunction. (Contributed by NM, 19-May-2007.)

Theorem3com12 1119 Commutation in antecedent. Swap 1st and 3rd. (Contributed by NM, 28-Jan-1996.) (Proof shortened by Andrew Salmon, 13-May-2011.)

Theorem3com13 1120 Commutation in antecedent. Swap 1st and 3rd. (Contributed by NM, 28-Jan-1996.)

Theorem3com23 1121 Commutation in antecedent. Swap 2nd and 3rd. (Contributed by NM, 28-Jan-1996.)

Theorem3coml 1122 Commutation in antecedent. Rotate left. (Contributed by NM, 28-Jan-1996.)

Theorem3comr 1123 Commutation in antecedent. Rotate right. (Contributed by NM, 28-Jan-1996.)

Theorem3adant3r1 1124 Deduction adding a conjunct to antecedent. (Contributed by NM, 16-Feb-2008.)

Theorem3adant3r2 1125 Deduction adding a conjunct to antecedent. (Contributed by NM, 17-Feb-2008.)

Theorem3adant3r3 1126 Deduction adding a conjunct to antecedent. (Contributed by NM, 18-Feb-2008.)

Theorem3an1rs 1127 Swap conjuncts. (Contributed by NM, 16-Dec-2007.)

Theorem3imp1 1128 Importation to left triple conjunction. (Contributed by NM, 24-Feb-2005.)

Theorem3impd 1129 Importation deduction for triple conjunction. (Contributed by NM, 26-Oct-2006.)

Theorem3imp2 1130 Importation to right triple conjunction. (Contributed by NM, 26-Oct-2006.)

Theorem3exp1 1131 Exportation from left triple conjunction. (Contributed by NM, 24-Feb-2005.)

Theorem3expd 1132 Exportation deduction for triple conjunction. (Contributed by NM, 26-Oct-2006.)

Theorem3exp2 1133 Exportation from right triple conjunction. (Contributed by NM, 26-Oct-2006.)

Theoremexp5o 1134 A triple exportation inference. (Contributed by Jeff Hankins, 8-Jul-2009.)

Theoremexp516 1135 A triple exportation inference. (Contributed by Jeff Hankins, 8-Jul-2009.)

Theoremexp520 1136 A triple exportation inference. (Contributed by Jeff Hankins, 8-Jul-2009.)

Theorem3anassrs 1137 Associative law for conjunction applied to antecedent (eliminates syllogism). (Contributed by Mario Carneiro, 4-Jan-2017.)

Theorem3adant1l 1138 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)

Theorem3adant1r 1139 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)

Theorem3adant2l 1140 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)

Theorem3adant2r 1141 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)

Theorem3adant3l 1142 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)

Theorem3adant3r 1143 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)

Theoremsyl12anc 1144 Syllogism combined with contraction. (Contributed by Jeff Hankins, 1-Aug-2009.)

Theoremsyl21anc 1145 Syllogism combined with contraction. (Contributed by Jeff Hankins, 1-Aug-2009.)

Theoremsyl3anc 1146 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl22anc 1147 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl13anc 1148 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl31anc 1149 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl112anc 1150 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl121anc 1151 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl211anc 1152 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl23anc 1153 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl32anc 1154 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl122anc 1155 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl212anc 1156 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl221anc 1157 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl113anc 1158 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl131anc 1159 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl311anc 1160 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl33anc 1161 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl222anc 1162 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl123anc 1163 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl132anc 1164 Syllogism combined with contraction. (Contributed by NM, 11-Jul-2012.)

Theoremsyl213anc 1165 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl231anc 1166 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl312anc 1167 Syllogism combined with contraction. (Contributed by NM, 11-Jul-2012.)

Theoremsyl321anc 1168 Syllogism combined with contraction. (Contributed by NM, 11-Jul-2012.)

Theoremsyl133anc 1169 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl313anc 1170 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl331anc 1171 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl223anc 1172 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl232anc 1173 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl322anc 1174 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl233anc 1175 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl323anc 1176 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl332anc 1177 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl333anc 1178 A syllogism inference combined with contraction. (Contributed by NM, 10-Mar-2012.)

Theoremsyl3an1 1179 A syllogism inference. (Contributed by NM, 22-Aug-1995.)

Theoremsyl3an2 1180 A syllogism inference. (Contributed by NM, 22-Aug-1995.)

Theoremsyl3an3 1181 A syllogism inference. (Contributed by NM, 22-Aug-1995.)

Theoremsyl3an1b 1182 A syllogism inference. (Contributed by NM, 22-Aug-1995.)

Theoremsyl3an2b 1183 A syllogism inference. (Contributed by NM, 22-Aug-1995.)

Theoremsyl3an3b 1184 A syllogism inference. (Contributed by NM, 22-Aug-1995.)

Theoremsyl3an1br 1185 A syllogism inference. (Contributed by NM, 22-Aug-1995.)

Theoremsyl3an2br 1186 A syllogism inference. (Contributed by NM, 22-Aug-1995.)

Theoremsyl3an3br 1187 A syllogism inference. (Contributed by NM, 22-Aug-1995.)

Theoremsyl3an 1188 A triple syllogism inference. (Contributed by NM, 13-May-2004.)

Theoremsyl3anb 1189 A triple syllogism inference. (Contributed by NM, 15-Oct-2005.)

Theoremsyl3anbr 1190 A triple syllogism inference. (Contributed by NM, 29-Dec-2011.)

Theoremsyld3an3 1191 A syllogism inference. (Contributed by NM, 20-May-2007.)

Theoremsyld3an1 1192 A syllogism inference. (Contributed by NM, 7-Jul-2008.)

Theoremsyld3an2 1193 A syllogism inference. (Contributed by NM, 20-May-2007.)

Theoremsyl3anl1 1194 A syllogism inference. (Contributed by NM, 24-Feb-2005.)

Theoremsyl3anl2 1195 A syllogism inference. (Contributed by NM, 24-Feb-2005.)

Theoremsyl3anl3 1196 A syllogism inference. (Contributed by NM, 24-Feb-2005.)

Theoremsyl3anl 1197 A triple syllogism inference. (Contributed by NM, 24-Dec-2006.)

Theoremsyl3anr1 1198 A syllogism inference. (Contributed by NM, 31-Jul-2007.)

Theoremsyl3anr2 1199 A syllogism inference. (Contributed by NM, 1-Aug-2007.)

Theoremsyl3anr3 1200 A syllogism inference. (Contributed by NM, 23-Aug-2007.)

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