Theorem bj-nexdt

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

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

Proof

Step	Hyp	Ref	Expression
1		nf5r	$$⊢Ⅎx\phi \to \left(\phi \to \forall x\phi \right)$$
2		bj-nexdh	$$⊢\forall x\left(\phi \to \neg \psi \right)\to \left(\left(\phi \to \forall x\phi \right)\to \left(\phi \to \neg \exists x\psi \right)\right)$$
3	1 2	syl5com	$$⊢Ⅎx\phi \to \left(\forall x\left(\phi \to \neg \psi \right)\to \left(\phi \to \neg \exists x\psi \right)\right)$$