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Metamath Proof Explorer

Theorem syl5ibrcom

Description: A mixed syllogism inference. (Contributed by NM, 20-Jun-2007)

Ref Expression
Hypotheses imbitrrid.1 ⊢ φ → θ
imbitrrid.2 ⊢ χ → ψ ↔ θ
Assertion syl5ibrcom ⊢ φ → χ → ψ

Proof

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