Metamath Proof Explorer

Theorem uunT12

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	uunT12.1	$⊢ (⊤ \land φ \land ψ) \to χ$
	Assertion	uunT12	$⊢ (φ \land ψ) \to χ$

Proof

Step	Hyp	Ref	Expression
1		uunT12.1	$⊢ (⊤ \land φ \land ψ) \to χ$
2		3anass	$⊢ (⊤ \land φ \land ψ) \leftrightarrow (⊤ \land (φ \land ψ))$
3		truan	$⊢ (⊤ \land (φ \land ψ)) \leftrightarrow (φ \land ψ)$
4	2 3	bitri	$⊢ (⊤ \land φ \land ψ) \leftrightarrow (φ \land ψ)$
5	4 1	sylbir	$⊢ (φ \land ψ) \to χ$