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Mirrors > Home > ILE Home > Th. List > simp12 | GIF version |
Description: Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.) |
Ref | Expression |
---|---|
simp12 | ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp2 1000 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜓) | |
2 | 1 | 3ad2ant1 1020 | 1 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜓) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ w3a 980 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 |
This theorem depends on definitions: df-bi 117 df-3an 982 |
This theorem is referenced by: simpl12 1075 simpr12 1084 simp112 1129 simp212 1138 simp312 1147 frecsuclem 6432 dvdsgcd 12048 coprimeprodsq 12292 pythagtriplem4 12303 pythagtriplem13 12311 pythagtriplem14 12312 pythagtriplem16 12314 pythagtrip 12318 pceu 12330 |
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