Metamath Proof Explorer

Theorem dfvd3anir

Description: Right-to-left inference form of dfvd3an . (Contributed by Alan Sare, 13-Jun-2015) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Hypothesis	dfvd3anir.1	$⊢ (φ \land ψ \land χ) \to θ$
	Assertion	dfvd3anir	$⊢ ((φ, ψ, χ) \to θ)$

Proof

Step	Hyp	Ref	Expression
1		dfvd3anir.1	$⊢ (φ \land ψ \land χ) \to θ$
2		dfvd3an	$⊢ ((φ, ψ, χ) \to θ) \leftrightarrow ((φ \land ψ \land χ) \to θ)$
3	1 2	mpbir	$⊢ ((φ, ψ, χ) \to θ)$