This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem dfvd2ir

Description: Right-to-left inference form of dfvd2 . (Contributed by Alan Sare, 14-Nov-2011) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Hypothesis	dfvd2ir.1	$⊢ φ \to (ψ \to χ)$
	Assertion	dfvd2ir	$⊢ (φ, ψ \to χ)$

Proof

Step	Hyp	Ref	Expression
1		dfvd2ir.1	$⊢ φ \to (ψ \to χ)$
2		dfvd2	$⊢ (φ, ψ \to χ) \leftrightarrow (φ \to (ψ \to χ))$
3	1 2	mpbir	$⊢ (φ, ψ \to χ)$