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Metamath Proof Explorer

Theorem sylan2i

Description: A syllogism inference. (Contributed by NM, 1-Aug-1994)

Ref Expression
Hypotheses sylan2i.1 ⊢ φ → θ
sylan2i.2 ⊢ ψ → χ ∧ θ → τ
Assertion sylan2i ⊢ ψ → χ ∧ φ → τ

Proof

Step Hyp Ref Expression
1 sylan2i.1 ⊢ φ → θ
2 sylan2i.2 ⊢ ψ → χ ∧ θ → τ
3 1 a1i ⊢ ψ → φ → θ
4 3 2 sylan2d ⊢ ψ → χ ∧ φ → τ