Metamath Proof Explorer

Theorem uunT11

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	uunT11.1	$⊢ (⊤ \land φ \land φ) \to ψ$
	Assertion	uunT11	$⊢ φ \to ψ$

Proof

Step	Hyp	Ref	Expression
1		uunT11.1	$⊢ (⊤ \land φ \land φ) \to ψ$
2		3anass	$⊢ (⊤ \land φ \land φ) \leftrightarrow (⊤ \land (φ \land φ))$
3		truan	$⊢ (⊤ \land (φ \land φ)) \leftrightarrow (φ \land φ)$
4		anidm	$⊢ (φ \land φ) \leftrightarrow φ$
5	2 3 4	3bitri	$⊢ (⊤ \land φ \land φ) \leftrightarrow φ$
6	5 1	sylbir	$⊢ φ \to ψ$