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Metamath Proof Explorer

Theorem syl7bi

Description: A mixed syllogism inference from a doubly nested implication and a biconditional. (Contributed by NM, 14-May-1993)

Ref Expression
Hypotheses syl7bi.1 ⊢ φ ↔ ψ
syl7bi.2 ⊢ χ → θ → ψ → τ
Assertion syl7bi ⊢ χ → θ → φ → τ

Proof

Step Hyp Ref Expression
1 syl7bi.1 ⊢ φ ↔ ψ
2 syl7bi.2 ⊢ χ → θ → ψ → τ
3 1 biimpi ⊢ φ → ψ
4 3 2 syl7 ⊢ χ → θ → φ → τ