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Mirrors > Home > ILE Home > Th. List > simp2r | GIF version |
Description: Simplification of triple conjunction. (Contributed by NM, 9-Nov-2011.) |
Ref | Expression |
---|---|
simp2r | ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpr 108 | . 2 ⊢ ((𝜓 ∧ 𝜒) → 𝜒) | |
2 | 1 | 3ad2ant2 960 | 1 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜒) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 102 ∧ w3a 919 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 |
This theorem depends on definitions: df-bi 115 df-3an 921 |
This theorem is referenced by: simpl2r 992 simpr2r 998 simp12r 1052 simp22r 1058 simp32r 1064 issod 4074 funprg 4969 fsnunf 5383 f1oiso2 5486 tfrlemibxssdm 5964 ecopovtrn 6226 ecopovtrng 6229 addassnqg 6572 ltsonq 6588 ltanqg 6590 ltmnqg 6591 addassnq0 6652 recexprlem1ssl 6823 mulasssrg 6935 distrsrg 6936 lttrsr 6939 ltsosr 6941 ltasrg 6947 mulextsr1lem 6956 mulextsr1 6957 axmulass 7039 axdistr 7040 dmdcanap 7810 lediv2 7969 ltdiv23 7970 lediv23 7971 expaddzaplem 9519 expaddzap 9520 expmulzap 9522 expdivap 9527 fldivndvdslt 10335 prmexpb 10530 |
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