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Metamath Proof Explorer

Theorem sylbid

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

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

Proof

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