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Mirrors > Home > ILE Home > Th. List > simp11 | GIF version |
Description: Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.) |
Ref | Expression |
---|---|
simp11 | ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp1 992 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜑) | |
2 | 1 | 3ad2ant1 1013 | 1 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜑) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ w3a 973 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 |
This theorem depends on definitions: df-bi 116 df-3an 975 |
This theorem is referenced by: simpl11 1067 simpr11 1076 simp111 1121 simp211 1130 simp311 1139 frecsuclem 6385 coprimeprodsq 12211 pythagtriplem14 12231 pythagtrip 12237 |
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