Metamath Proof Explorer

Theorem uun132p1

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	uun132p1.1	$⊢ ((ψ \land χ) \land φ) \to θ$
	Assertion	uun132p1	$⊢ (φ \land ψ \land χ) \to θ$

Proof

Step	Hyp	Ref	Expression
1		uun132p1.1	$⊢ ((ψ \land χ) \land φ) \to θ$
2		3anass	$⊢ (φ \land ψ \land χ) \leftrightarrow (φ \land (ψ \land χ))$
3		ancom	$⊢ (φ \land (ψ \land χ)) \leftrightarrow ((ψ \land χ) \land φ)$
4	2 3	bitri	$⊢ (φ \land ψ \land χ) \leftrightarrow ((ψ \land χ) \land φ)$
5	4 1	sylbi	$⊢ (φ \land ψ \land χ) \to θ$