uunT12p5

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	uunT12p5.1	$⊢ (ψ \land φ \land ⊤) \to χ$
	Assertion	uunT12p5	$⊢ (φ \land ψ) \to χ$

Proof

Step	Hyp	Ref	Expression
1		uunT12p5.1	$⊢ (ψ \land φ \land ⊤) \to χ$
2		3anrev	$⊢ (ψ \land φ \land ⊤) \leftrightarrow (⊤ \land φ \land ψ)$
3		3anass	$⊢ (⊤ \land φ \land ψ) \leftrightarrow (⊤ \land (φ \land ψ))$
4	2 3	bitri	$⊢ (ψ \land φ \land ⊤) \leftrightarrow (⊤ \land (φ \land ψ))$
5		truan	$⊢ (⊤ \land (φ \land ψ)) \leftrightarrow (φ \land ψ)$
6	4 5	bitri	$⊢ (ψ \land φ \land ⊤) \leftrightarrow (φ \land ψ)$
7	6 1	sylbir	$⊢ (φ \land ψ) \to χ$

Metamath Proof Explorer

Theorem uunT12p5

Proof