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Metamath Proof Explorer

Theorem bj-nexdvt

Description: Closed form of nexdv . (Contributed by BJ, 20-Oct-2019)

		Ref	Expression
	Assertion	bj-nexdvt	$⊢ \forall x (φ \to \neg ψ) \to (φ \to \neg \exists x ψ)$

Step	Hyp	Ref	Expression
1		nfv	$⊢ Ⅎ x φ$
2		bj-nexdt	$⊢ Ⅎ x φ \to (\forall x (φ \to \neg ψ) \to (φ \to \neg \exists x ψ))$
3	1 2	ax-mp	$⊢ \forall x (φ \to \neg ψ) \to (φ \to \neg \exists x ψ)$