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Metamath Proof Explorer

Theorem sylan2b

Description: A syllogism inference. (Contributed by NM, 21-Apr-1994)

Ref Expression
Hypotheses sylan2b.1 ⊢ φ ↔ χ
sylan2b.2 ⊢ ψ ∧ χ → θ
Assertion sylan2b ⊢ ψ ∧ φ → θ

Proof

Step Hyp Ref Expression
1 sylan2b.1 ⊢ φ ↔ χ
2 sylan2b.2 ⊢ ψ ∧ χ → θ
3 1 biimpi ⊢ φ → χ
4 3 2 sylan2 ⊢ ψ ∧ φ → θ