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Mirrors > Home > ILE Home > Th. List > simp13 | GIF version |
Description: Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.) |
Ref | Expression |
---|---|
simp13 | ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp3 945 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜒) | |
2 | 1 | 3ad2ant1 964 | 1 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜒) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ w3a 924 |
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 926 |
This theorem is referenced by: simpl13 1020 simpr13 1029 simp113 1074 simp213 1083 simp313 1092 funtpg 5065 dvdsgcd 11279 |
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