Metamath Proof Explorer

Theorem uun111

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	uun111.1	$⊢ (φ \land φ \land φ) \to ψ$
	Assertion	uun111	$⊢ φ \to ψ$

Proof

Step	Hyp	Ref	Expression
1		uun111.1	$⊢ (φ \land φ \land φ) \to ψ$
2		3anass	$⊢ (φ \land φ \land φ) \leftrightarrow (φ \land (φ \land φ))$
3		anabs5	$⊢ (φ \land (φ \land φ)) \leftrightarrow (φ \land φ)$
4		anidm	$⊢ (φ \land φ) \leftrightarrow φ$
5	2 3 4	3bitri	$⊢ (φ \land φ \land φ) \leftrightarrow φ$
6	5 1	sylbir	$⊢ φ \to ψ$