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Metamath Proof Explorer

Theorem syl5ibcom

Description: A mixed syllogism inference. (Contributed by NM, 19-Jun-2007)

Ref Expression
Hypotheses imbitrid.1 ⊢ φ → ψ
imbitrid.2 ⊢ χ → ψ ↔ θ
Assertion syl5ibcom ⊢ φ → χ → θ

Proof

Step Hyp Ref Expression
1 imbitrid.1 ⊢ φ → ψ
2 imbitrid.2 ⊢ χ → ψ ↔ θ
3 1 2 imbitrid ⊢ χ → φ → θ
4 3 com12 ⊢ φ → χ → θ