Theorem bj-nexdvt

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

	Ref	Expression
Assertion	bj-nexdvt	$$⊢\forall x\left(\phi \to \neg \psi \right)\to \left(\phi \to \neg \exists x\psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		nfv	$$⊢Ⅎx\phi$$
2		bj-nexdt	$$⊢Ⅎx\phi \to \left(\forall x\left(\phi \to \neg \psi \right)\to \left(\phi \to \neg \exists x\psi \right)\right)$$
3	1 2	ax-mp	$$⊢\forall x\left(\phi \to \neg \psi \right)\to \left(\phi \to \neg \exists x\psi \right)$$