P. 11 of Theorem List - Intuitionistic Logic Explorer

Theorem List for Intuitionistic Logic Explorer - 1001-1100   *Has distinct variable group(s)

Type	Label	Description
Statement
Theorem	simp1ll 1001	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ( ph /\ ps ) /\ ch ) /\ th /\ ta ) -> ph )
Theorem	simp1lr 1002	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ( ph /\ ps ) /\ ch ) /\ th /\ ta ) -> ps )
Theorem	simp1rl 1003	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ch /\ ( ph /\ ps ) ) /\ th /\ ta ) -> ph )
Theorem	simp1rr 1004	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ch /\ ( ph /\ ps ) ) /\ th /\ ta ) -> ps )
Theorem	simp2ll 1005	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( th /\ ( ( ph /\ ps ) /\ ch ) /\ ta ) -> ph )
Theorem	simp2lr 1006	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( th /\ ( ( ph /\ ps ) /\ ch ) /\ ta ) -> ps )
Theorem	simp2rl 1007	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( th /\ ( ch /\ ( ph /\ ps ) ) /\ ta ) -> ph )
Theorem	simp2rr 1008	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( th /\ ( ch /\ ( ph /\ ps ) ) /\ ta ) -> ps )
Theorem	simp3ll 1009	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( th /\ ta /\ ( ( ph /\ ps ) /\ ch ) ) -> ph )
Theorem	simp3lr 1010	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( th /\ ta /\ ( ( ph /\ ps ) /\ ch ) ) -> ps )
Theorem	simp3rl 1011	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( th /\ ta /\ ( ch /\ ( ph /\ ps ) ) ) -> ph )
Theorem	simp3rr 1012	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( th /\ ta /\ ( ch /\ ( ph /\ ps ) ) ) -> ps )
Theorem	simpl11 1013	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) /\ et ) -> ph )
Theorem	simpl12 1014	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) /\ et ) -> ps )
Theorem	simpl13 1015	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) /\ et ) -> ch )
Theorem	simpl21 1016	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( th /\ ( ph /\ ps /\ ch ) /\ ta ) /\ et ) -> ph )
Theorem	simpl22 1017	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( th /\ ( ph /\ ps /\ ch ) /\ ta ) /\ et ) -> ps )
Theorem	simpl23 1018	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( th /\ ( ph /\ ps /\ ch ) /\ ta ) /\ et ) -> ch )
Theorem	simpl31 1019	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( th /\ ta /\ ( ph /\ ps /\ ch ) ) /\ et ) -> ph )
Theorem	simpl32 1020	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( th /\ ta /\ ( ph /\ ps /\ ch ) ) /\ et ) -> ps )
Theorem	simpl33 1021	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( th /\ ta /\ ( ph /\ ps /\ ch ) ) /\ et ) -> ch )
Theorem	simpr11 1022	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ( ( ph /\ ps /\ ch ) /\ th /\ ta ) ) -> ph )
Theorem	simpr12 1023	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ( ( ph /\ ps /\ ch ) /\ th /\ ta ) ) -> ps )
Theorem	simpr13 1024	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ( ( ph /\ ps /\ ch ) /\ th /\ ta ) ) -> ch )
Theorem	simpr21 1025	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ( th /\ ( ph /\ ps /\ ch ) /\ ta ) ) -> ph )
Theorem	simpr22 1026	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ( th /\ ( ph /\ ps /\ ch ) /\ ta ) ) -> ps )
Theorem	simpr23 1027	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ( th /\ ( ph /\ ps /\ ch ) /\ ta ) ) -> ch )
Theorem	simpr31 1028	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ( th /\ ta /\ ( ph /\ ps /\ ch ) ) ) -> ph )
Theorem	simpr32 1029	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ( th /\ ta /\ ( ph /\ ps /\ ch ) ) ) -> ps )
Theorem	simpr33 1030	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ( th /\ ta /\ ( ph /\ ps /\ ch ) ) ) -> ch )
Theorem	simp1l1 1031	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ( ph /\ ps /\ ch ) /\ th ) /\ ta /\ et ) -> ph )
Theorem	simp1l2 1032	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ( ph /\ ps /\ ch ) /\ th ) /\ ta /\ et ) -> ps )
Theorem	simp1l3 1033	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ( ph /\ ps /\ ch ) /\ th ) /\ ta /\ et ) -> ch )
Theorem	simp1r1 1034	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( th /\ ( ph /\ ps /\ ch ) ) /\ ta /\ et ) -> ph )
Theorem	simp1r2 1035	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( th /\ ( ph /\ ps /\ ch ) ) /\ ta /\ et ) -> ps )
Theorem	simp1r3 1036	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( th /\ ( ph /\ ps /\ ch ) ) /\ ta /\ et ) -> ch )
Theorem	simp2l1 1037	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ ( ( ph /\ ps /\ ch ) /\ th ) /\ et ) -> ph )
Theorem	simp2l2 1038	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ ( ( ph /\ ps /\ ch ) /\ th ) /\ et ) -> ps )
Theorem	simp2l3 1039	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ ( ( ph /\ ps /\ ch ) /\ th ) /\ et ) -> ch )
Theorem	simp2r1 1040	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ ( th /\ ( ph /\ ps /\ ch ) ) /\ et ) -> ph )
Theorem	simp2r2 1041	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ ( th /\ ( ph /\ ps /\ ch ) ) /\ et ) -> ps )
Theorem	simp2r3 1042	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ ( th /\ ( ph /\ ps /\ ch ) ) /\ et ) -> ch )
Theorem	simp3l1 1043	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ et /\ ( ( ph /\ ps /\ ch ) /\ th ) ) -> ph )
Theorem	simp3l2 1044	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ et /\ ( ( ph /\ ps /\ ch ) /\ th ) ) -> ps )
Theorem	simp3l3 1045	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ et /\ ( ( ph /\ ps /\ ch ) /\ th ) ) -> ch )
Theorem	simp3r1 1046	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ et /\ ( th /\ ( ph /\ ps /\ ch ) ) ) -> ph )
Theorem	simp3r2 1047	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ et /\ ( th /\ ( ph /\ ps /\ ch ) ) ) -> ps )
Theorem	simp3r3 1048	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ et /\ ( th /\ ( ph /\ ps /\ ch ) ) ) -> ch )
Theorem	simp11l 1049	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ( ph /\ ps ) /\ ch /\ th ) /\ ta /\ et ) -> ph )
Theorem	simp11r 1050	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ( ph /\ ps ) /\ ch /\ th ) /\ ta /\ et ) -> ps )
Theorem	simp12l 1051	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ch /\ ( ph /\ ps ) /\ th ) /\ ta /\ et ) -> ph )
Theorem	simp12r 1052	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ch /\ ( ph /\ ps ) /\ th ) /\ ta /\ et ) -> ps )
Theorem	simp13l 1053	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ch /\ th /\ ( ph /\ ps ) ) /\ ta /\ et ) -> ph )
Theorem	simp13r 1054	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ch /\ th /\ ( ph /\ ps ) ) /\ ta /\ et ) -> ps )
Theorem	simp21l 1055	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ ( ( ph /\ ps ) /\ ch /\ th ) /\ et ) -> ph )
Theorem	simp21r 1056	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ ( ( ph /\ ps ) /\ ch /\ th ) /\ et ) -> ps )
Theorem	simp22l 1057	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ ( ch /\ ( ph /\ ps ) /\ th ) /\ et ) -> ph )
Theorem	simp22r 1058	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ ( ch /\ ( ph /\ ps ) /\ th ) /\ et ) -> ps )
Theorem	simp23l 1059	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ ( ch /\ th /\ ( ph /\ ps ) ) /\ et ) -> ph )
Theorem	simp23r 1060	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ ( ch /\ th /\ ( ph /\ ps ) ) /\ et ) -> ps )
Theorem	simp31l 1061	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ et /\ ( ( ph /\ ps ) /\ ch /\ th ) ) -> ph )
Theorem	simp31r 1062	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ et /\ ( ( ph /\ ps ) /\ ch /\ th ) ) -> ps )
Theorem	simp32l 1063	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ et /\ ( ch /\ ( ph /\ ps ) /\ th ) ) -> ph )
Theorem	simp32r 1064	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ et /\ ( ch /\ ( ph /\ ps ) /\ th ) ) -> ps )
Theorem	simp33l 1065	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ et /\ ( ch /\ th /\ ( ph /\ ps ) ) ) -> ph )
Theorem	simp33r 1066	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ et /\ ( ch /\ th /\ ( ph /\ ps ) ) ) -> ps )
Theorem	simp111 1067	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) /\ et /\ ze ) -> ph )
Theorem	simp112 1068	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) /\ et /\ ze ) -> ps )
Theorem	simp113 1069	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) /\ et /\ ze ) -> ch )
Theorem	simp121 1070	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( th /\ ( ph /\ ps /\ ch ) /\ ta ) /\ et /\ ze ) -> ph )
Theorem	simp122 1071	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( th /\ ( ph /\ ps /\ ch ) /\ ta ) /\ et /\ ze ) -> ps )
Theorem	simp123 1072	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( th /\ ( ph /\ ps /\ ch ) /\ ta ) /\ et /\ ze ) -> ch )
Theorem	simp131 1073	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( th /\ ta /\ ( ph /\ ps /\ ch ) ) /\ et /\ ze ) -> ph )
Theorem	simp132 1074	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( th /\ ta /\ ( ph /\ ps /\ ch ) ) /\ et /\ ze ) -> ps )
Theorem	simp133 1075	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( th /\ ta /\ ( ph /\ ps /\ ch ) ) /\ et /\ ze ) -> ch )
Theorem	simp211 1076	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ( ( ph /\ ps /\ ch ) /\ th /\ ta ) /\ ze ) -> ph )
Theorem	simp212 1077	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ( ( ph /\ ps /\ ch ) /\ th /\ ta ) /\ ze ) -> ps )
Theorem	simp213 1078	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ( ( ph /\ ps /\ ch ) /\ th /\ ta ) /\ ze ) -> ch )
Theorem	simp221 1079	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ( th /\ ( ph /\ ps /\ ch ) /\ ta ) /\ ze ) -> ph )
Theorem	simp222 1080	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ( th /\ ( ph /\ ps /\ ch ) /\ ta ) /\ ze ) -> ps )
Theorem	simp223 1081	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ( th /\ ( ph /\ ps /\ ch ) /\ ta ) /\ ze ) -> ch )
Theorem	simp231 1082	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ( th /\ ta /\ ( ph /\ ps /\ ch ) ) /\ ze ) -> ph )
Theorem	simp232 1083	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ( th /\ ta /\ ( ph /\ ps /\ ch ) ) /\ ze ) -> ps )
Theorem	simp233 1084	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ( th /\ ta /\ ( ph /\ ps /\ ch ) ) /\ ze ) -> ch )
Theorem	simp311 1085	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ze /\ ( ( ph /\ ps /\ ch ) /\ th /\ ta ) ) -> ph )
Theorem	simp312 1086	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ze /\ ( ( ph /\ ps /\ ch ) /\ th /\ ta ) ) -> ps )
Theorem	simp313 1087	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ze /\ ( ( ph /\ ps /\ ch ) /\ th /\ ta ) ) -> ch )
Theorem	simp321 1088	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ze /\ ( th /\ ( ph /\ ps /\ ch ) /\ ta ) ) -> ph )
Theorem	simp322 1089	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ze /\ ( th /\ ( ph /\ ps /\ ch ) /\ ta ) ) -> ps )
Theorem	simp323 1090	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ze /\ ( th /\ ( ph /\ ps /\ ch ) /\ ta ) ) -> ch )
Theorem	simp331 1091	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ze /\ ( th /\ ta /\ ( ph /\ ps /\ ch ) ) ) -> ph )
Theorem	simp332 1092	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ze /\ ( th /\ ta /\ ( ph /\ ps /\ ch ) ) ) -> ps )
Theorem	simp333 1093	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ze /\ ( th /\ ta /\ ( ph /\ ps /\ ch ) ) ) -> ch )
Theorem	3adantl1 1094	Deduction adding a conjunct to antecedent. (Contributed by NM, 24-Feb-2005.)
|- ( ( ( ph /\ ps ) /\ ch ) -> th )   =>    |- ( ( ( ta /\ ph /\ ps ) /\ ch ) -> th )
Theorem	3adantl2 1095	Deduction adding a conjunct to antecedent. (Contributed by NM, 24-Feb-2005.)
|- ( ( ( ph /\ ps ) /\ ch ) -> th )   =>    |- ( ( ( ph /\ ta /\ ps ) /\ ch ) -> th )
Theorem	3adantl3 1096	Deduction adding a conjunct to antecedent. (Contributed by NM, 24-Feb-2005.)
|- ( ( ( ph /\ ps ) /\ ch ) -> th )   =>    |- ( ( ( ph /\ ps /\ ta ) /\ ch ) -> th )
Theorem	3adantr1 1097	Deduction adding a conjunct to antecedent. (Contributed by NM, 27-Apr-2005.)
|- ( ( ph /\ ( ps /\ ch ) ) -> th )   =>    |- ( ( ph /\ ( ta /\ ps /\ ch ) ) -> th )
Theorem	3adantr2 1098	Deduction adding a conjunct to antecedent. (Contributed by NM, 27-Apr-2005.)
|- ( ( ph /\ ( ps /\ ch ) ) -> th )   =>    |- ( ( ph /\ ( ps /\ ta /\ ch ) ) -> th )
Theorem	3adantr3 1099	Deduction adding a conjunct to antecedent. (Contributed by NM, 27-Apr-2005.)
|- ( ( ph /\ ( ps /\ ch ) ) -> th )   =>    |- ( ( ph /\ ( ps /\ ch /\ ta ) ) -> th )
Theorem	3ad2antl1 1100	Deduction adding conjuncts to antecedent. (Contributed by NM, 4-Aug-2007.)
|- ( ( ph /\ ch ) -> th )   =>    |- ( ( ( ph /\ ps /\ ta ) /\ ch ) -> th )