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Metamath Proof Explorer

Theorem un01

Description: A unionizing deduction. (Contributed by Alan Sare, 28-Apr-2015) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Hypothesis	un01.1	$⊢ ((⊤, φ) \to ψ)$
	Assertion	un01	$⊢ (φ \to ψ)$

Step	Hyp	Ref	Expression
1		un01.1	$⊢ ((⊤, φ) \to ψ)$
2		tru	$⊢ ⊤$
3	2	jctl	$⊢ φ \to (⊤ \land φ)$
4	1	dfvd2ani	$⊢ (⊤ \land φ) \to ψ$
5	3 4	syl	$⊢ φ \to ψ$
6	5	dfvd1ir	$⊢ (φ \to ψ)$