Metamath Proof Explorer

Theorem sylan2i

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

		Ref	Expression
	Hypotheses	sylan2i.1	$⊢ φ \to θ$
		sylan2i.2	$⊢ ψ \to ((χ \land θ) \to τ)$
	Assertion	sylan2i	$⊢ ψ \to ((χ \land φ) \to τ)$

Proof

Step	Hyp	Ref	Expression
1		sylan2i.1	$⊢ φ \to θ$
2		sylan2i.2	$⊢ ψ \to ((χ \land θ) \to τ)$
3	1	a1i	$⊢ ψ \to (φ \to θ)$
4	3 2	sylan2d	$⊢ ψ \to ((χ \land φ) \to τ)$