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Theorem List for New Foundations Explorer - 1001-1100   *Has distinct variable group(s)
TypeLabelDescription
Statement

Theoremsimprl2 1001 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ ((φ ψ χ) θ)) → ψ)

Theoremsimprl3 1002 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ ((φ ψ χ) θ)) → χ)

Theoremsimprr1 1003 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ (θ (φ ψ χ))) → φ)

Theoremsimprr2 1004 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ (θ (φ ψ χ))) → ψ)

Theoremsimprr3 1005 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ (θ (φ ψ χ))) → χ)

Theoremsimpl1l 1006 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((φ ψ) χ θ) τ) → φ)

Theoremsimpl1r 1007 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((φ ψ) χ θ) τ) → ψ)

Theoremsimpl2l 1008 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((χ (φ ψ) θ) τ) → φ)

Theoremsimpl2r 1009 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((χ (φ ψ) θ) τ) → ψ)

Theoremsimpl3l 1010 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((χ θ (φ ψ)) τ) → φ)

Theoremsimpl3r 1011 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((χ θ (φ ψ)) τ) → ψ)

Theoremsimpr1l 1012 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ ((φ ψ) χ θ)) → φ)

Theoremsimpr1r 1013 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ ((φ ψ) χ θ)) → ψ)

Theoremsimpr2l 1014 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ (χ (φ ψ) θ)) → φ)

Theoremsimpr2r 1015 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ (χ (φ ψ) θ)) → ψ)

Theoremsimpr3l 1016 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ (χ θ (φ ψ))) → φ)

Theoremsimpr3r 1017 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ (χ θ (φ ψ))) → ψ)

Theoremsimp1ll 1018 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((φ ψ) χ) θ τ) → φ)

Theoremsimp1lr 1019 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((φ ψ) χ) θ τ) → ψ)

Theoremsimp1rl 1020 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((χ (φ ψ)) θ τ) → φ)

Theoremsimp1rr 1021 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((χ (φ ψ)) θ τ) → ψ)

Theoremsimp2ll 1022 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((θ ((φ ψ) χ) τ) → φ)

Theoremsimp2lr 1023 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((θ ((φ ψ) χ) τ) → ψ)

Theoremsimp2rl 1024 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((θ (χ (φ ψ)) τ) → φ)

Theoremsimp2rr 1025 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((θ (χ (φ ψ)) τ) → ψ)

Theoremsimp3ll 1026 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((θ τ ((φ ψ) χ)) → φ)

Theoremsimp3lr 1027 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((θ τ ((φ ψ) χ)) → ψ)

Theoremsimp3rl 1028 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((θ τ (χ (φ ψ))) → φ)

Theoremsimp3rr 1029 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((θ τ (χ (φ ψ))) → ψ)

Theoremsimpl11 1030 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((φ ψ χ) θ τ) η) → φ)

Theoremsimpl12 1031 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((φ ψ χ) θ τ) η) → ψ)

Theoremsimpl13 1032 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((φ ψ χ) θ τ) η) → χ)

Theoremsimpl21 1033 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((θ (φ ψ χ) τ) η) → φ)

Theoremsimpl22 1034 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((θ (φ ψ χ) τ) η) → ψ)

Theoremsimpl23 1035 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((θ (φ ψ χ) τ) η) → χ)

Theoremsimpl31 1036 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((θ τ (φ ψ χ)) η) → φ)

Theoremsimpl32 1037 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((θ τ (φ ψ χ)) η) → ψ)

Theoremsimpl33 1038 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((θ τ (φ ψ χ)) η) → χ)

Theoremsimpr11 1039 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((η ((φ ψ χ) θ τ)) → φ)

Theoremsimpr12 1040 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((η ((φ ψ χ) θ τ)) → ψ)

Theoremsimpr13 1041 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((η ((φ ψ χ) θ τ)) → χ)

Theoremsimpr21 1042 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((η (θ (φ ψ χ) τ)) → φ)

Theoremsimpr22 1043 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((η (θ (φ ψ χ) τ)) → ψ)

Theoremsimpr23 1044 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((η (θ (φ ψ χ) τ)) → χ)

Theoremsimpr31 1045 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((η (θ τ (φ ψ χ))) → φ)

Theoremsimpr32 1046 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((η (θ τ (φ ψ χ))) → ψ)

Theoremsimpr33 1047 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((η (θ τ (φ ψ χ))) → χ)

Theoremsimp1l1 1048 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((φ ψ χ) θ) τ η) → φ)

Theoremsimp1l2 1049 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((φ ψ χ) θ) τ η) → ψ)

Theoremsimp1l3 1050 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((φ ψ χ) θ) τ η) → χ)

Theoremsimp1r1 1051 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((θ (φ ψ χ)) τ η) → φ)

Theoremsimp1r2 1052 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((θ (φ ψ χ)) τ η) → ψ)

Theoremsimp1r3 1053 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((θ (φ ψ χ)) τ η) → χ)

Theoremsimp2l1 1054 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ ((φ ψ χ) θ) η) → φ)

Theoremsimp2l2 1055 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ ((φ ψ χ) θ) η) → ψ)

Theoremsimp2l3 1056 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ ((φ ψ χ) θ) η) → χ)

Theoremsimp2r1 1057 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ (θ (φ ψ χ)) η) → φ)

Theoremsimp2r2 1058 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ (θ (φ ψ χ)) η) → ψ)

Theoremsimp2r3 1059 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ (θ (φ ψ χ)) η) → χ)

Theoremsimp3l1 1060 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ η ((φ ψ χ) θ)) → φ)

Theoremsimp3l2 1061 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ η ((φ ψ χ) θ)) → ψ)

Theoremsimp3l3 1062 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ η ((φ ψ χ) θ)) → χ)

Theoremsimp3r1 1063 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ η (θ (φ ψ χ))) → φ)

Theoremsimp3r2 1064 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ η (θ (φ ψ χ))) → ψ)

Theoremsimp3r3 1065 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ η (θ (φ ψ χ))) → χ)

Theoremsimp11l 1066 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((φ ψ) χ θ) τ η) → φ)

Theoremsimp11r 1067 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((φ ψ) χ θ) τ η) → ψ)

Theoremsimp12l 1068 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((χ (φ ψ) θ) τ η) → φ)

Theoremsimp12r 1069 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((χ (φ ψ) θ) τ η) → ψ)

Theoremsimp13l 1070 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((χ θ (φ ψ)) τ η) → φ)

Theoremsimp13r 1071 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((χ θ (φ ψ)) τ η) → ψ)

Theoremsimp21l 1072 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ ((φ ψ) χ θ) η) → φ)

Theoremsimp21r 1073 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ ((φ ψ) χ θ) η) → ψ)

Theoremsimp22l 1074 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ (χ (φ ψ) θ) η) → φ)

Theoremsimp22r 1075 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ (χ (φ ψ) θ) η) → ψ)

Theoremsimp23l 1076 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ (χ θ (φ ψ)) η) → φ)

Theoremsimp23r 1077 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ (χ θ (φ ψ)) η) → ψ)

Theoremsimp31l 1078 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ η ((φ ψ) χ θ)) → φ)

Theoremsimp31r 1079 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ η ((φ ψ) χ θ)) → ψ)

Theoremsimp32l 1080 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ η (χ (φ ψ) θ)) → φ)

Theoremsimp32r 1081 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ η (χ (φ ψ) θ)) → ψ)

Theoremsimp33l 1082 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ η (χ θ (φ ψ))) → φ)

Theoremsimp33r 1083 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ η (χ θ (φ ψ))) → ψ)

Theoremsimp111 1084 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((φ ψ χ) θ τ) η ζ) → φ)

Theoremsimp112 1085 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((φ ψ χ) θ τ) η ζ) → ψ)

Theoremsimp113 1086 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((φ ψ χ) θ τ) η ζ) → χ)

Theoremsimp121 1087 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((θ (φ ψ χ) τ) η ζ) → φ)

Theoremsimp122 1088 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((θ (φ ψ χ) τ) η ζ) → ψ)

Theoremsimp123 1089 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((θ (φ ψ χ) τ) η ζ) → χ)

Theoremsimp131 1090 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((θ τ (φ ψ χ)) η ζ) → φ)

Theoremsimp132 1091 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((θ τ (φ ψ χ)) η ζ) → ψ)

Theoremsimp133 1092 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((θ τ (φ ψ χ)) η ζ) → χ)

Theoremsimp211 1093 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((η ((φ ψ χ) θ τ) ζ) → φ)

Theoremsimp212 1094 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((η ((φ ψ χ) θ τ) ζ) → ψ)

Theoremsimp213 1095 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((η ((φ ψ χ) θ τ) ζ) → χ)

Theoremsimp221 1096 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((η (θ (φ ψ χ) τ) ζ) → φ)

Theoremsimp222 1097 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((η (θ (φ ψ χ) τ) ζ) → ψ)

Theoremsimp223 1098 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((η (θ (φ ψ χ) τ) ζ) → χ)

Theoremsimp231 1099 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((η (θ τ (φ ψ χ)) ζ) → φ)

Theoremsimp232 1100 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((η (θ τ (φ ψ χ)) ζ) → ψ)

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