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Metamath Proof Explorer

Theorem biimtrrid

Description: A mixed syllogism inference from a nested implication and a biconditional. (Contributed by NM, 21-Jun-1993)

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

Proof

Step Hyp Ref Expression
1 biimtrrid.1 ⊢ ψ ↔ φ
2 biimtrrid.2 ⊢ χ → ψ → θ
3 1 biimpri ⊢ φ → ψ
4 3 2 syl5 ⊢ χ → φ → θ