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Theorem List for Intuitionistic Logic Explorer - 901-1000   *Has distinct variable group(s)
TypeLabelDescription
Statement
 
Theoremsimp3i 901 Infer a conjunct from a triple conjunction. (Contributed by NM, 19-Apr-2005.)
(φ ψ χ)       χ
 
Theoremsimp1d 902 Deduce a conjunct from a triple conjunction. (Contributed by NM, 4-Sep-2005.)
(φ → (ψ χ θ))       (φψ)
 
Theoremsimp2d 903 Deduce a conjunct from a triple conjunction. (Contributed by NM, 4-Sep-2005.)
(φ → (ψ χ θ))       (φχ)
 
Theoremsimp3d 904 Deduce a conjunct from a triple conjunction. (Contributed by NM, 4-Sep-2005.)
(φ → (ψ χ θ))       (φθ)
 
Theoremsimp1bi 905 Deduce a conjunct from a triple conjunction. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)
(φ ↔ (ψ χ θ))       (φψ)
 
Theoremsimp2bi 906 Deduce a conjunct from a triple conjunction. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)
(φ ↔ (ψ χ θ))       (φχ)
 
Theoremsimp3bi 907 Deduce a conjunct from a triple conjunction. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)
(φ ↔ (ψ χ θ))       (φθ)
 
Theorem3adant1 908 Deduction adding a conjunct to antecedent. (Contributed by NM, 16-Jul-1995.)
((φ ψ) → χ)       ((θ φ ψ) → χ)
 
Theorem3adant2 909 Deduction adding a conjunct to antecedent. (Contributed by NM, 16-Jul-1995.)
((φ ψ) → χ)       ((φ θ ψ) → χ)
 
Theorem3adant3 910 Deduction adding a conjunct to antecedent. (Contributed by NM, 16-Jul-1995.)
((φ ψ) → χ)       ((φ ψ θ) → χ)
 
Theorem3ad2ant1 911 Deduction adding conjuncts to an antecedent. (Contributed by NM, 21-Apr-2005.)
(φχ)       ((φ ψ θ) → χ)
 
Theorem3ad2ant2 912 Deduction adding conjuncts to an antecedent. (Contributed by NM, 21-Apr-2005.)
(φχ)       ((ψ φ θ) → χ)
 
Theorem3ad2ant3 913 Deduction adding conjuncts to an antecedent. (Contributed by NM, 21-Apr-2005.)
(φχ)       ((ψ θ φ) → χ)
 
Theoremsimp1l 914 Simplification of triple conjunction. (Contributed by NM, 9-Nov-2011.)
(((φ ψ) χ θ) → φ)
 
Theoremsimp1r 915 Simplification of triple conjunction. (Contributed by NM, 9-Nov-2011.)
(((φ ψ) χ θ) → ψ)
 
Theoremsimp2l 916 Simplification of triple conjunction. (Contributed by NM, 9-Nov-2011.)
((φ (ψ χ) θ) → ψ)
 
Theoremsimp2r 917 Simplification of triple conjunction. (Contributed by NM, 9-Nov-2011.)
((φ (ψ χ) θ) → χ)
 
Theoremsimp3l 918 Simplification of triple conjunction. (Contributed by NM, 9-Nov-2011.)
((φ ψ (χ θ)) → χ)
 
Theoremsimp3r 919 Simplification of triple conjunction. (Contributed by NM, 9-Nov-2011.)
((φ ψ (χ θ)) → θ)
 
Theoremsimp11 920 Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
(((φ ψ χ) θ τ) → φ)
 
Theoremsimp12 921 Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
(((φ ψ χ) θ τ) → ψ)
 
Theoremsimp13 922 Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
(((φ ψ χ) θ τ) → χ)
 
Theoremsimp21 923 Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
((φ (ψ χ θ) τ) → ψ)
 
Theoremsimp22 924 Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
((φ (ψ χ θ) τ) → χ)
 
Theoremsimp23 925 Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
((φ (ψ χ θ) τ) → θ)
 
Theoremsimp31 926 Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
((φ ψ (χ θ τ)) → χ)
 
Theoremsimp32 927 Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
((φ ψ (χ θ τ)) → θ)
 
Theoremsimp33 928 Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
((φ ψ (χ θ τ)) → τ)
 
Theoremsimpll1 929 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((φ ψ χ) θ) τ) → φ)
 
Theoremsimpll2 930 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((φ ψ χ) θ) τ) → ψ)
 
Theoremsimpll3 931 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((φ ψ χ) θ) τ) → χ)
 
Theoremsimplr1 932 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((θ (φ ψ χ)) τ) → φ)
 
Theoremsimplr2 933 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((θ (φ ψ χ)) τ) → ψ)
 
Theoremsimplr3 934 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((θ (φ ψ χ)) τ) → χ)
 
Theoremsimprl1 935 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ ((φ ψ χ) θ)) → φ)
 
Theoremsimprl2 936 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ ((φ ψ χ) θ)) → ψ)
 
Theoremsimprl3 937 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ ((φ ψ χ) θ)) → χ)
 
Theoremsimprr1 938 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ (θ (φ ψ χ))) → φ)
 
Theoremsimprr2 939 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ (θ (φ ψ χ))) → ψ)
 
Theoremsimprr3 940 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ (θ (φ ψ χ))) → χ)
 
Theoremsimpl1l 941 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((φ ψ) χ θ) τ) → φ)
 
Theoremsimpl1r 942 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((φ ψ) χ θ) τ) → ψ)
 
Theoremsimpl2l 943 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((χ (φ ψ) θ) τ) → φ)
 
Theoremsimpl2r 944 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((χ (φ ψ) θ) τ) → ψ)
 
Theoremsimpl3l 945 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((χ θ (φ ψ)) τ) → φ)
 
Theoremsimpl3r 946 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((χ θ (φ ψ)) τ) → ψ)
 
Theoremsimpr1l 947 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ ((φ ψ) χ θ)) → φ)
 
Theoremsimpr1r 948 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ ((φ ψ) χ θ)) → ψ)
 
Theoremsimpr2l 949 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ (χ (φ ψ) θ)) → φ)
 
Theoremsimpr2r 950 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ (χ (φ ψ) θ)) → ψ)
 
Theoremsimpr3l 951 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ (χ θ (φ ψ))) → φ)
 
Theoremsimpr3r 952 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ (χ θ (φ ψ))) → ψ)
 
Theoremsimp1ll 953 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((φ ψ) χ) θ τ) → φ)
 
Theoremsimp1lr 954 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((φ ψ) χ) θ τ) → ψ)
 
Theoremsimp1rl 955 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((χ (φ ψ)) θ τ) → φ)
 
Theoremsimp1rr 956 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((χ (φ ψ)) θ τ) → ψ)
 
Theoremsimp2ll 957 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((θ ((φ ψ) χ) τ) → φ)
 
Theoremsimp2lr 958 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((θ ((φ ψ) χ) τ) → ψ)
 
Theoremsimp2rl 959 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((θ (χ (φ ψ)) τ) → φ)
 
Theoremsimp2rr 960 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((θ (χ (φ ψ)) τ) → ψ)
 
Theoremsimp3ll 961 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((θ τ ((φ ψ) χ)) → φ)
 
Theoremsimp3lr 962 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((θ τ ((φ ψ) χ)) → ψ)
 
Theoremsimp3rl 963 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((θ τ (χ (φ ψ))) → φ)
 
Theoremsimp3rr 964 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((θ τ (χ (φ ψ))) → ψ)
 
Theoremsimpl11 965 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((φ ψ χ) θ τ) η) → φ)
 
Theoremsimpl12 966 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((φ ψ χ) θ τ) η) → ψ)
 
Theoremsimpl13 967 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((φ ψ χ) θ τ) η) → χ)
 
Theoremsimpl21 968 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((θ (φ ψ χ) τ) η) → φ)
 
Theoremsimpl22 969 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((θ (φ ψ χ) τ) η) → ψ)
 
Theoremsimpl23 970 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((θ (φ ψ χ) τ) η) → χ)
 
Theoremsimpl31 971 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((θ τ (φ ψ χ)) η) → φ)
 
Theoremsimpl32 972 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((θ τ (φ ψ χ)) η) → ψ)
 
Theoremsimpl33 973 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((θ τ (φ ψ χ)) η) → χ)
 
Theoremsimpr11 974 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((η ((φ ψ χ) θ τ)) → φ)
 
Theoremsimpr12 975 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((η ((φ ψ χ) θ τ)) → ψ)
 
Theoremsimpr13 976 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((η ((φ ψ χ) θ τ)) → χ)
 
Theoremsimpr21 977 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((η (θ (φ ψ χ) τ)) → φ)
 
Theoremsimpr22 978 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((η (θ (φ ψ χ) τ)) → ψ)
 
Theoremsimpr23 979 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((η (θ (φ ψ χ) τ)) → χ)
 
Theoremsimpr31 980 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((η (θ τ (φ ψ χ))) → φ)
 
Theoremsimpr32 981 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((η (θ τ (φ ψ χ))) → ψ)
 
Theoremsimpr33 982 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((η (θ τ (φ ψ χ))) → χ)
 
Theoremsimp1l1 983 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((φ ψ χ) θ) τ η) → φ)
 
Theoremsimp1l2 984 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((φ ψ χ) θ) τ η) → ψ)
 
Theoremsimp1l3 985 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((φ ψ χ) θ) τ η) → χ)
 
Theoremsimp1r1 986 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((θ (φ ψ χ)) τ η) → φ)
 
Theoremsimp1r2 987 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((θ (φ ψ χ)) τ η) → ψ)
 
Theoremsimp1r3 988 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((θ (φ ψ χ)) τ η) → χ)
 
Theoremsimp2l1 989 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ ((φ ψ χ) θ) η) → φ)
 
Theoremsimp2l2 990 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ ((φ ψ χ) θ) η) → ψ)
 
Theoremsimp2l3 991 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ ((φ ψ χ) θ) η) → χ)
 
Theoremsimp2r1 992 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ (θ (φ ψ χ)) η) → φ)
 
Theoremsimp2r2 993 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ (θ (φ ψ χ)) η) → ψ)
 
Theoremsimp2r3 994 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ (θ (φ ψ χ)) η) → χ)
 
Theoremsimp3l1 995 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ η ((φ ψ χ) θ)) → φ)
 
Theoremsimp3l2 996 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ η ((φ ψ χ) θ)) → ψ)
 
Theoremsimp3l3 997 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ η ((φ ψ χ) θ)) → χ)
 
Theoremsimp3r1 998 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ η (θ (φ ψ χ))) → φ)
 
Theoremsimp3r2 999 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ η (θ (φ ψ χ))) → ψ)
 
Theoremsimp3r3 1000 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((τ η (θ (φ ψ χ))) → χ)
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