Metamath Proof Explorer

Theorem syld3an3

Description: A syllogism inference. (Contributed by NM, 20-May-2007)

		Ref	Expression
	Hypotheses	syld3an3.1	$⊢ (φ \land ψ \land χ) \to θ$
		syld3an3.2	$⊢ (φ \land ψ \land θ) \to τ$
	Assertion	syld3an3	$⊢ (φ \land ψ \land χ) \to τ$

Proof

Step	Hyp	Ref	Expression
1		syld3an3.1	$⊢ (φ \land ψ \land χ) \to θ$
2		syld3an3.2	$⊢ (φ \land ψ \land θ) \to τ$
3		simp1	$⊢ (φ \land ψ \land χ) \to φ$
4		simp2	$⊢ (φ \land ψ \land χ) \to ψ$
5	3 4 1 2	syl3anc	$⊢ (φ \land ψ \land χ) \to τ$