Metamath Proof Explorer

Theorem uunT1p1

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	uunT1p1.1	$⊢ (φ \land ⊤) \to ψ$
	Assertion	uunT1p1	$⊢ φ \to ψ$

Proof

Step	Hyp	Ref	Expression
1		uunT1p1.1	$⊢ (φ \land ⊤) \to ψ$
2		ancom	$⊢ (φ \land ⊤) \leftrightarrow (⊤ \land φ)$
3		truan	$⊢ (⊤ \land φ) \leftrightarrow φ$
4	2 3	bitri	$⊢ (φ \land ⊤) \leftrightarrow φ$
5	4 1	sylbir	$⊢ φ \to ψ$