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Mirrors > Home > ILE Home > Th. List > simp31 | GIF version |
Description: Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.) |
Ref | Expression |
---|---|
simp31 | ⊢ ((𝜑 ∧ 𝜓 ∧ (𝜒 ∧ 𝜃 ∧ 𝜏)) → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp1 904 | . 2 ⊢ ((𝜒 ∧ 𝜃 ∧ 𝜏) → 𝜒) | |
2 | 1 | 3ad2ant3 927 | 1 ⊢ ((𝜑 ∧ 𝜓 ∧ (𝜒 ∧ 𝜃 ∧ 𝜏)) → 𝜒) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ w3a 885 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 |
This theorem depends on definitions: df-bi 110 df-3an 887 |
This theorem is referenced by: simpl31 985 simpr31 994 simp131 1039 simp231 1048 simp331 1057 |
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