P. 12 of Theorem List - Intuitionistic Logic Explorer

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

Type	Label	Description
Statement
Theorem	simp22r 1101	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ ( ch /\ ( ph /\ ps ) /\ th ) /\ et ) -> ps )
Theorem	simp23l 1102	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ ( ch /\ th /\ ( ph /\ ps ) ) /\ et ) -> ph )
Theorem	simp23r 1103	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ ( ch /\ th /\ ( ph /\ ps ) ) /\ et ) -> ps )
Theorem	simp31l 1104	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ et /\ ( ( ph /\ ps ) /\ ch /\ th ) ) -> ph )
Theorem	simp31r 1105	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ et /\ ( ( ph /\ ps ) /\ ch /\ th ) ) -> ps )
Theorem	simp32l 1106	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ et /\ ( ch /\ ( ph /\ ps ) /\ th ) ) -> ph )
Theorem	simp32r 1107	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ et /\ ( ch /\ ( ph /\ ps ) /\ th ) ) -> ps )
Theorem	simp33l 1108	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ et /\ ( ch /\ th /\ ( ph /\ ps ) ) ) -> ph )
Theorem	simp33r 1109	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ et /\ ( ch /\ th /\ ( ph /\ ps ) ) ) -> ps )
Theorem	simp111 1110	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) /\ et /\ ze ) -> ph )
Theorem	simp112 1111	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) /\ et /\ ze ) -> ps )
Theorem	simp113 1112	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) /\ et /\ ze ) -> ch )
Theorem	simp121 1113	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( th /\ ( ph /\ ps /\ ch ) /\ ta ) /\ et /\ ze ) -> ph )
Theorem	simp122 1114	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( th /\ ( ph /\ ps /\ ch ) /\ ta ) /\ et /\ ze ) -> ps )
Theorem	simp123 1115	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( th /\ ( ph /\ ps /\ ch ) /\ ta ) /\ et /\ ze ) -> ch )
Theorem	simp131 1116	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( th /\ ta /\ ( ph /\ ps /\ ch ) ) /\ et /\ ze ) -> ph )
Theorem	simp132 1117	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( th /\ ta /\ ( ph /\ ps /\ ch ) ) /\ et /\ ze ) -> ps )
Theorem	simp133 1118	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( th /\ ta /\ ( ph /\ ps /\ ch ) ) /\ et /\ ze ) -> ch )
Theorem	simp211 1119	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ( ( ph /\ ps /\ ch ) /\ th /\ ta ) /\ ze ) -> ph )
Theorem	simp212 1120	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ( ( ph /\ ps /\ ch ) /\ th /\ ta ) /\ ze ) -> ps )
Theorem	simp213 1121	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ( ( ph /\ ps /\ ch ) /\ th /\ ta ) /\ ze ) -> ch )
Theorem	simp221 1122	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ( th /\ ( ph /\ ps /\ ch ) /\ ta ) /\ ze ) -> ph )
Theorem	simp222 1123	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ( th /\ ( ph /\ ps /\ ch ) /\ ta ) /\ ze ) -> ps )
Theorem	simp223 1124	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ( th /\ ( ph /\ ps /\ ch ) /\ ta ) /\ ze ) -> ch )
Theorem	simp231 1125	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ( th /\ ta /\ ( ph /\ ps /\ ch ) ) /\ ze ) -> ph )
Theorem	simp232 1126	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ( th /\ ta /\ ( ph /\ ps /\ ch ) ) /\ ze ) -> ps )
Theorem	simp233 1127	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ( th /\ ta /\ ( ph /\ ps /\ ch ) ) /\ ze ) -> ch )
Theorem	simp311 1128	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ze /\ ( ( ph /\ ps /\ ch ) /\ th /\ ta ) ) -> ph )
Theorem	simp312 1129	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ze /\ ( ( ph /\ ps /\ ch ) /\ th /\ ta ) ) -> ps )
Theorem	simp313 1130	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ze /\ ( ( ph /\ ps /\ ch ) /\ th /\ ta ) ) -> ch )
Theorem	simp321 1131	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ze /\ ( th /\ ( ph /\ ps /\ ch ) /\ ta ) ) -> ph )
Theorem	simp322 1132	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ze /\ ( th /\ ( ph /\ ps /\ ch ) /\ ta ) ) -> ps )
Theorem	simp323 1133	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ze /\ ( th /\ ( ph /\ ps /\ ch ) /\ ta ) ) -> ch )
Theorem	simp331 1134	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ze /\ ( th /\ ta /\ ( ph /\ ps /\ ch ) ) ) -> ph )
Theorem	simp332 1135	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ze /\ ( th /\ ta /\ ( ph /\ ps /\ ch ) ) ) -> ps )
Theorem	simp333 1136	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ze /\ ( th /\ ta /\ ( ph /\ ps /\ ch ) ) ) -> ch )
Theorem	3adantl1 1137	Deduction adding a conjunct to antecedent. (Contributed by NM, 24-Feb-2005.)
|- ( ( ( ph /\ ps ) /\ ch ) -> th )   =>    |- ( ( ( ta /\ ph /\ ps ) /\ ch ) -> th )
Theorem	3adantl2 1138	Deduction adding a conjunct to antecedent. (Contributed by NM, 24-Feb-2005.)
|- ( ( ( ph /\ ps ) /\ ch ) -> th )   =>    |- ( ( ( ph /\ ta /\ ps ) /\ ch ) -> th )
Theorem	3adantl3 1139	Deduction adding a conjunct to antecedent. (Contributed by NM, 24-Feb-2005.)
|- ( ( ( ph /\ ps ) /\ ch ) -> th )   =>    |- ( ( ( ph /\ ps /\ ta ) /\ ch ) -> th )
Theorem	3adantr1 1140	Deduction adding a conjunct to antecedent. (Contributed by NM, 27-Apr-2005.)
|- ( ( ph /\ ( ps /\ ch ) ) -> th )   =>    |- ( ( ph /\ ( ta /\ ps /\ ch ) ) -> th )
Theorem	3adantr2 1141	Deduction adding a conjunct to antecedent. (Contributed by NM, 27-Apr-2005.)
|- ( ( ph /\ ( ps /\ ch ) ) -> th )   =>    |- ( ( ph /\ ( ps /\ ta /\ ch ) ) -> th )
Theorem	3adantr3 1142	Deduction adding a conjunct to antecedent. (Contributed by NM, 27-Apr-2005.)
|- ( ( ph /\ ( ps /\ ch ) ) -> th )   =>    |- ( ( ph /\ ( ps /\ ch /\ ta ) ) -> th )
Theorem	3ad2antl1 1143	Deduction adding conjuncts to antecedent. (Contributed by NM, 4-Aug-2007.)
|- ( ( ph /\ ch ) -> th )   =>    |- ( ( ( ph /\ ps /\ ta ) /\ ch ) -> th )
Theorem	3ad2antl2 1144	Deduction adding conjuncts to antecedent. (Contributed by NM, 4-Aug-2007.)
|- ( ( ph /\ ch ) -> th )   =>    |- ( ( ( ps /\ ph /\ ta ) /\ ch ) -> th )
Theorem	3ad2antl3 1145	Deduction adding conjuncts to antecedent. (Contributed by NM, 4-Aug-2007.)
|- ( ( ph /\ ch ) -> th )   =>    |- ( ( ( ps /\ ta /\ ph ) /\ ch ) -> th )
Theorem	3ad2antr1 1146	Deduction adding a conjuncts to antecedent. (Contributed by NM, 25-Dec-2007.)
|- ( ( ph /\ ch ) -> th )   =>    |- ( ( ph /\ ( ch /\ ps /\ ta ) ) -> th )
Theorem	3ad2antr2 1147	Deduction adding a conjuncts to antecedent. (Contributed by NM, 27-Dec-2007.)
|- ( ( ph /\ ch ) -> th )   =>    |- ( ( ph /\ ( ps /\ ch /\ ta ) ) -> th )
Theorem	3ad2antr3 1148	Deduction adding a conjuncts to antecedent. (Contributed by NM, 30-Dec-2007.)
|- ( ( ph /\ ch ) -> th )   =>    |- ( ( ph /\ ( ps /\ ta /\ ch ) ) -> th )
Theorem	3anibar 1149	Remove a hypothesis from the second member of a biimplication. (Contributed by FL, 22-Jul-2008.)
|- ( ( ph /\ ps /\ ch ) -> ( th <-> ( ch /\ ta ) ) )   =>    |- ( ( ph /\ ps /\ ch ) -> ( th <-> ta ) )
Theorem	3mix1 1150	Introduction in triple disjunction. (Contributed by NM, 4-Apr-1995.)
|- ( ph -> ( ph \/ ps \/ ch ) )
Theorem	3mix2 1151	Introduction in triple disjunction. (Contributed by NM, 4-Apr-1995.)
|- ( ph -> ( ps \/ ph \/ ch ) )
Theorem	3mix3 1152	Introduction in triple disjunction. (Contributed by NM, 4-Apr-1995.)
|- ( ph -> ( ps \/ ch \/ ph ) )
Theorem	3mix1i 1153	Introduction in triple disjunction. (Contributed by Mario Carneiro, 6-Oct-2014.)
|- ph   =>    |- ( ph \/ ps \/ ch )
Theorem	3mix2i 1154	Introduction in triple disjunction. (Contributed by Mario Carneiro, 6-Oct-2014.)
|- ph   =>    |- ( ps \/ ph \/ ch )
Theorem	3mix3i 1155	Introduction in triple disjunction. (Contributed by Mario Carneiro, 6-Oct-2014.)
|- ph   =>    |- ( ps \/ ch \/ ph )
Theorem	3mix1d 1156	Deduction introducing triple disjunction. (Contributed by Scott Fenton, 8-Jun-2011.)
|- ( ph -> ps )   =>    |- ( ph -> ( ps \/ ch \/ th ) )
Theorem	3mix2d 1157	Deduction introducing triple disjunction. (Contributed by Scott Fenton, 8-Jun-2011.)
|- ( ph -> ps )   =>    |- ( ph -> ( ch \/ ps \/ th ) )
Theorem	3mix3d 1158	Deduction introducing triple disjunction. (Contributed by Scott Fenton, 8-Jun-2011.)
|- ( ph -> ps )   =>    |- ( ph -> ( ch \/ th \/ ps ) )
Theorem	3pm3.2i 1159	Infer conjunction of premises. (Contributed by NM, 10-Feb-1995.)
|- ph   &    |- ps   &    |- ch   =>    |- ( ph /\ ps /\ ch )
Theorem	pm3.2an3 1160	pm3.2 138 for a triple conjunction. (Contributed by Alan Sare, 24-Oct-2011.)
|- ( ph -> ( ps -> ( ch -> ( ph /\ ps /\ ch ) ) ) )
Theorem	3jca 1161	Join consequents with conjunction. (Contributed by NM, 9-Apr-1994.)
|- ( ph -> ps )   &    |- ( ph -> ch )   &    |- ( ph -> th )   =>    |- ( ph -> ( ps /\ ch /\ th ) )
Theorem	3jcad 1162	Deduction conjoining the consequents of three implications. (Contributed by NM, 25-Sep-2005.)
|- ( ph -> ( ps -> ch ) )   &    |- ( ph -> ( ps -> th ) )   &    |- ( ph -> ( ps -> ta ) )   =>    |- ( ph -> ( ps -> ( ch /\ th /\ ta ) ) )
Theorem	mpbir3an 1163	Detach a conjunction of truths in a biconditional. (Contributed by NM, 16-Sep-2011.) (Revised by NM, 9-Jan-2015.)
|- ps   &    |- ch   &    |- th   &    |- ( ph <-> ( ps /\ ch /\ th ) )   =>    |- ph
Theorem	mpbir3and 1164	Detach a conjunction of truths in a biconditional. (Contributed by Mario Carneiro, 11-May-2014.)
|- ( ph -> ch )   &    |- ( ph -> th )   &    |- ( ph -> ta )   &    |- ( ph -> ( ps <-> ( ch /\ th /\ ta ) ) )   =>    |- ( ph -> ps )
Theorem	syl3anbrc 1165	Syllogism inference. (Contributed by Mario Carneiro, 11-May-2014.)
|- ( ph -> ps )   &    |- ( ph -> ch )   &    |- ( ph -> th )   &    |- ( ta <-> ( ps /\ ch /\ th ) )   =>    |- ( ph -> ta )
Theorem	3anim123i 1166	Join antecedents and consequents with conjunction. (Contributed by NM, 8-Apr-1994.)
|- ( ph -> ps )   &    |- ( ch -> th )   &    |- ( ta -> et )   =>    |- ( ( ph /\ ch /\ ta ) -> ( ps /\ th /\ et ) )
Theorem	3anim1i 1167	Add two conjuncts to antecedent and consequent. (Contributed by Jeff Hankins, 16-Aug-2009.)
|- ( ph -> ps )   =>    |- ( ( ph /\ ch /\ th ) -> ( ps /\ ch /\ th ) )
Theorem	3anim2i 1168	Add two conjuncts to antecedent and consequent. (Contributed by AV, 21-Nov-2019.)
|- ( ph -> ps )   =>    |- ( ( ch /\ ph /\ th ) -> ( ch /\ ps /\ th ) )
Theorem	3anim3i 1169	Add two conjuncts to antecedent and consequent. (Contributed by Jeff Hankins, 19-Aug-2009.)
|- ( ph -> ps )   =>    |- ( ( ch /\ th /\ ph ) -> ( ch /\ th /\ ps ) )
Theorem	3anbi123i 1170	Join 3 biconditionals with conjunction. (Contributed by NM, 21-Apr-1994.)
|- ( ph <-> ps )   &    |- ( ch <-> th )   &    |- ( ta <-> et )   =>    |- ( ( ph /\ ch /\ ta ) <-> ( ps /\ th /\ et ) )
Theorem	3orbi123i 1171	Join 3 biconditionals with disjunction. (Contributed by NM, 17-May-1994.)
|- ( ph <-> ps )   &    |- ( ch <-> th )   &    |- ( ta <-> et )   =>    |- ( ( ph \/ ch \/ ta ) <-> ( ps \/ th \/ et ) )
Theorem	3anbi1i 1172	Inference adding two conjuncts to each side of a biconditional. (Contributed by NM, 8-Sep-2006.)
|- ( ph <-> ps )   =>    |- ( ( ph /\ ch /\ th ) <-> ( ps /\ ch /\ th ) )
Theorem	3anbi2i 1173	Inference adding two conjuncts to each side of a biconditional. (Contributed by NM, 8-Sep-2006.)
|- ( ph <-> ps )   =>    |- ( ( ch /\ ph /\ th ) <-> ( ch /\ ps /\ th ) )
Theorem	3anbi3i 1174	Inference adding two conjuncts to each side of a biconditional. (Contributed by NM, 8-Sep-2006.)
|- ( ph <-> ps )   =>    |- ( ( ch /\ th /\ ph ) <-> ( ch /\ th /\ ps ) )
Theorem	3imp 1175	Importation inference. (Contributed by NM, 8-Apr-1994.)
|- ( ph -> ( ps -> ( ch -> th ) ) )   =>    |- ( ( ph /\ ps /\ ch ) -> th )
Theorem	3impa 1176	Importation from double to triple conjunction. (Contributed by NM, 20-Aug-1995.)
|- ( ( ( ph /\ ps ) /\ ch ) -> th )   =>    |- ( ( ph /\ ps /\ ch ) -> th )
Theorem	3impb 1177	Importation from double to triple conjunction. (Contributed by NM, 20-Aug-1995.)
|- ( ( ph /\ ( ps /\ ch ) ) -> th )   =>    |- ( ( ph /\ ps /\ ch ) -> th )
Theorem	3impia 1178	Importation to triple conjunction. (Contributed by NM, 13-Jun-2006.)
|- ( ( ph /\ ps ) -> ( ch -> th ) )   =>    |- ( ( ph /\ ps /\ ch ) -> th )
Theorem	3impib 1179	Importation to triple conjunction. (Contributed by NM, 13-Jun-2006.)
|- ( ph -> ( ( ps /\ ch ) -> th ) )   =>    |- ( ( ph /\ ps /\ ch ) -> th )
Theorem	3exp 1180	Exportation inference. (Contributed by NM, 30-May-1994.)
|- ( ( ph /\ ps /\ ch ) -> th )   =>    |- ( ph -> ( ps -> ( ch -> th ) ) )
Theorem	3expa 1181	Exportation from triple to double conjunction. (Contributed by NM, 20-Aug-1995.)
|- ( ( ph /\ ps /\ ch ) -> th )   =>    |- ( ( ( ph /\ ps ) /\ ch ) -> th )
Theorem	3expb 1182	Exportation from triple to double conjunction. (Contributed by NM, 20-Aug-1995.)
|- ( ( ph /\ ps /\ ch ) -> th )   =>    |- ( ( ph /\ ( ps /\ ch ) ) -> th )
Theorem	3expia 1183	Exportation from triple conjunction. (Contributed by NM, 19-May-2007.)
|- ( ( ph /\ ps /\ ch ) -> th )   =>    |- ( ( ph /\ ps ) -> ( ch -> th ) )
Theorem	3expib 1184	Exportation from triple conjunction. (Contributed by NM, 19-May-2007.)
|- ( ( ph /\ ps /\ ch ) -> th )   =>    |- ( ph -> ( ( ps /\ ch ) -> th ) )
Theorem	3com12 1185	Commutation in antecedent. Swap 1st and 3rd. (Contributed by NM, 28-Jan-1996.) (Proof shortened by Andrew Salmon, 13-May-2011.)
|- ( ( ph /\ ps /\ ch ) -> th )   =>    |- ( ( ps /\ ph /\ ch ) -> th )
Theorem	3com13 1186	Commutation in antecedent. Swap 1st and 3rd. (Contributed by NM, 28-Jan-1996.)
|- ( ( ph /\ ps /\ ch ) -> th )   =>    |- ( ( ch /\ ps /\ ph ) -> th )
Theorem	3com23 1187	Commutation in antecedent. Swap 2nd and 3rd. (Contributed by NM, 28-Jan-1996.)
|- ( ( ph /\ ps /\ ch ) -> th )   =>    |- ( ( ph /\ ch /\ ps ) -> th )
Theorem	3coml 1188	Commutation in antecedent. Rotate left. (Contributed by NM, 28-Jan-1996.)
|- ( ( ph /\ ps /\ ch ) -> th )   =>    |- ( ( ps /\ ch /\ ph ) -> th )
Theorem	3comr 1189	Commutation in antecedent. Rotate right. (Contributed by NM, 28-Jan-1996.)
|- ( ( ph /\ ps /\ ch ) -> th )   =>    |- ( ( ch /\ ph /\ ps ) -> th )
Theorem	3adant3r1 1190	Deduction adding a conjunct to antecedent. (Contributed by NM, 16-Feb-2008.)
|- ( ( ph /\ ps /\ ch ) -> th )   =>    |- ( ( ph /\ ( ta /\ ps /\ ch ) ) -> th )
Theorem	3adant3r2 1191	Deduction adding a conjunct to antecedent. (Contributed by NM, 17-Feb-2008.)
|- ( ( ph /\ ps /\ ch ) -> th )   =>    |- ( ( ph /\ ( ps /\ ta /\ ch ) ) -> th )
Theorem	3adant3r3 1192	Deduction adding a conjunct to antecedent. (Contributed by NM, 18-Feb-2008.)
|- ( ( ph /\ ps /\ ch ) -> th )   =>    |- ( ( ph /\ ( ps /\ ch /\ ta ) ) -> th )
Theorem	ad4ant123 1193	Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.) (Proof shortened by Wolf Lammen, 14-Apr-2022.)
|- ( ( ph /\ ps /\ ch ) -> th )   =>    |- ( ( ( ( ph /\ ps ) /\ ch ) /\ ta ) -> th )
Theorem	ad4ant124 1194	Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.) (Proof shortened by Wolf Lammen, 14-Apr-2022.)
|- ( ( ph /\ ps /\ ch ) -> th )   =>    |- ( ( ( ( ph /\ ps ) /\ ta ) /\ ch ) -> th )
Theorem	ad4ant134 1195	Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.) (Proof shortened by Wolf Lammen, 14-Apr-2022.)
|- ( ( ph /\ ps /\ ch ) -> th )   =>    |- ( ( ( ( ph /\ ta ) /\ ps ) /\ ch ) -> th )
Theorem	ad4ant234 1196	Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.) (Proof shortened by Wolf Lammen, 14-Apr-2022.)
|- ( ( ph /\ ps /\ ch ) -> th )   =>    |- ( ( ( ( ta /\ ph ) /\ ps ) /\ ch ) -> th )
Theorem	3an1rs 1197	Swap conjuncts. (Contributed by NM, 16-Dec-2007.)
|- ( ( ( ph /\ ps /\ ch ) /\ th ) -> ta )   =>    |- ( ( ( ph /\ ps /\ th ) /\ ch ) -> ta )
Theorem	3imp1 1198	Importation to left triple conjunction. (Contributed by NM, 24-Feb-2005.)
|- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )   =>    |- ( ( ( ph /\ ps /\ ch ) /\ th ) -> ta )
Theorem	3impd 1199	Importation deduction for triple conjunction. (Contributed by NM, 26-Oct-2006.)
|- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )   =>    |- ( ph -> ( ( ps /\ ch /\ th ) -> ta ) )
Theorem	3imp2 1200	Importation to right triple conjunction. (Contributed by NM, 26-Oct-2006.)
|- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )   =>    |- ( ( ph /\ ( ps /\ ch /\ th ) ) -> ta )