Theorem bj-biexex

Description: When ph is substituted for ps , both sides express a form of nonfreeness. (Contributed by BJ, 20-Oct-2019)

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

Proof

Step	Hyp	Ref	Expression
1		nfe1	$$⊢Ⅎx\exists x\psi$$
2	1	19.23	$$⊢\forall x\left(\phi \to \exists x\psi \right)\leftrightarrow \left(\exists x\phi \to \exists x\psi \right)$$