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Metamath Proof Explorer

Theorem dfvd2anir

Description: Right-to-left inference form of dfvd2an . (Contributed by Alan Sare, 23-Apr-2015) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Hypothesis	dfvd2anir.1	$⊢ (φ \land ψ) \to χ$
	Assertion	dfvd2anir	$⊢ ((φ, ψ) \to χ)$

Proof

Step	Hyp	Ref	Expression
1		dfvd2anir.1	$⊢ (φ \land ψ) \to χ$
2		dfvd2an	$⊢ ((φ, ψ) \to χ) \leftrightarrow ((φ \land ψ) \to χ)$
3	1 2	mpbir	$⊢ ((φ, ψ) \to χ)$