Theorem bj-nexdh2

Description: Uncurried (imported) form of bj-nexdh . (Contributed by BJ, 6-May-2019)

	Ref	Expression
Assertion	bj-nexdh2	$$⊢\left(\forall x\left(\phi \to \neg \psi \right)\wedge \left(\chi \to \forall x\phi \right)\right)\to \left(\chi \to \neg \exists x\psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		bj-nexdh	$$⊢\forall x\left(\phi \to \neg \psi \right)\to \left(\left(\chi \to \forall x\phi \right)\to \left(\chi \to \neg \exists x\psi \right)\right)$$
2	1	imp	$$⊢\left(\forall x\left(\phi \to \neg \psi \right)\wedge \left(\chi \to \forall x\phi \right)\right)\to \left(\chi \to \neg \exists x\psi \right)$$