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Metamath Proof Explorer

Theorem sylibrd

Description: A syllogism deduction. (Contributed by NM, 3-Aug-1994)

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

Proof

Step Hyp Ref Expression
1 sylibrd.1 ⊢ φ → ψ → χ
2 sylibrd.2 ⊢ φ → θ ↔ χ
3 2 biimprd ⊢ φ → χ → θ
4 1 3 syld ⊢ φ → ψ → θ