Metamath Proof Explorer

Theorem 3impdirp1

Description: A deduction unionizing a non-unionized collection of virtual hypotheses. Commuted version of 3impdir . (Contributed by Alan Sare, 4-Feb-2017) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Hypothesis	3impdirp1.1	$⊢ ((χ \land ψ) \land (φ \land ψ)) \to θ$
	Assertion	3impdirp1	$⊢ (φ \land χ \land ψ) \to θ$

Proof

Step	Hyp	Ref	Expression
1		3impdirp1.1	$⊢ ((χ \land ψ) \land (φ \land ψ)) \to θ$
2		ancom	$⊢ ((χ \land ψ) \land (φ \land ψ)) \leftrightarrow ((φ \land ψ) \land (χ \land ψ))$
3	2 1	sylbir	$⊢ ((φ \land ψ) \land (χ \land ψ)) \to θ$
4	3	3impdir	$⊢ (φ \land χ \land ψ) \to θ$