Metamath Proof Explorer

Theorem uun2131p1

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

		Ref	Expression
	Hypothesis	uun2131p1.1	$⊢ ((φ \land χ) \land (φ \land ψ)) \to θ$
	Assertion	uun2131p1	$⊢ (φ \land ψ \land χ) \to θ$

Proof

Step	Hyp	Ref	Expression
1		uun2131p1.1	$⊢ ((φ \land χ) \land (φ \land ψ)) \to θ$
2		ancom	$⊢ ((φ \land ψ) \land (φ \land χ)) \leftrightarrow ((φ \land χ) \land (φ \land ψ))$
3	2 1	sylbi	$⊢ ((φ \land ψ) \land (φ \land χ)) \to θ$
4	3	3impdi	$⊢ (φ \land ψ \land χ) \to θ$