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Metamath Proof Explorer

Theorem imbitrdi

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

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

Proof

Step Hyp Ref Expression
1 imbitrdi.1 ⊢ φ → ψ → χ
2 imbitrdi.2 ⊢ χ ↔ θ
3 2 biimpi ⊢ χ → θ
4 1 3 syl6 ⊢ φ → ψ → θ