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Metamath Proof Explorer

Theorem imbitrrid

Description: A mixed syllogism inference. (Contributed by NM, 3-Apr-1994)

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

Proof

Step Hyp Ref Expression
1 imbitrrid.1 ⊢ φ → θ
2 imbitrrid.2 ⊢ χ → ψ ↔ θ
3 2 bicomd ⊢ χ → θ ↔ ψ
4 1 3 imbitrid ⊢ χ → φ → ψ