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Metamath Proof Explorer

Theorem biimtrdi

Description: A mixed syllogism inference. (Contributed by NM, 2-Jan-1994)

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

Proof

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