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Metamath Proof Explorer

Theorem dfvd3ani

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

		Ref	Expression
	Hypothesis	dfvd3ani.1	$⊢ ((φ, ψ, χ) \to θ)$
	Assertion	dfvd3ani	$⊢ (φ \land ψ \land χ) \to θ$

Step	Hyp	Ref	Expression
1		dfvd3ani.1	$⊢ ((φ, ψ, χ) \to θ)$
2		dfvd3an	$⊢ ((φ, ψ, χ) \to θ) \leftrightarrow ((φ \land ψ \land χ) \to θ)$
3	1 2	mpbi	$⊢ (φ \land ψ \land χ) \to θ$