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Mirrors > Home > ILE Home > Th. List > simp32 | GIF version |
Description: Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.) |
Ref | Expression |
---|---|
simp32 | ⊢ ((𝜑 ∧ 𝜓 ∧ (𝜒 ∧ 𝜃 ∧ 𝜏)) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp2 939 | . 2 ⊢ ((𝜒 ∧ 𝜃 ∧ 𝜏) → 𝜃) | |
2 | 1 | 3ad2ant3 961 | 1 ⊢ ((𝜑 ∧ 𝜓 ∧ (𝜒 ∧ 𝜃 ∧ 𝜏)) → 𝜃) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ 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: simpl32 1020 simpr32 1029 simp132 1074 simp232 1083 simp332 1092 |
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