uunTT1p1

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	uunTT1p1.1	$⊢ (⊤ \land φ \land ⊤) \to ψ$
	Assertion	uunTT1p1	$⊢ φ \to ψ$

Proof

Step	Hyp	Ref	Expression
1		uunTT1p1.1	$⊢ (⊤ \land φ \land ⊤) \to ψ$
2		3ancomb	$⊢ (⊤ \land φ \land ⊤) \leftrightarrow (⊤ \land ⊤ \land φ)$
3		3anass	$⊢ (⊤ \land ⊤ \land φ) \leftrightarrow (⊤ \land (⊤ \land φ))$
4		anabs5	$⊢ (⊤ \land (⊤ \land φ)) \leftrightarrow (⊤ \land φ)$
5	2 3 4	3bitri	$⊢ (⊤ \land φ \land ⊤) \leftrightarrow (⊤ \land φ)$
6		truan	$⊢ (⊤ \land φ) \leftrightarrow φ$
7	5 6	bitri	$⊢ (⊤ \land φ \land ⊤) \leftrightarrow φ$
8	7 1	sylbir	$⊢ φ \to ψ$

Metamath Proof Explorer

Theorem uunTT1p1

Proof