Theorem bj-cbvexivw

Description: Change bound variable. This is to cbvexvw what cbvalivw is to cbvalvw . TODO: move after cbvalivw . (Contributed by BJ, 17-Mar-2020)

	Ref	Expression
Hypothesis	bj-cbvexivw.1	$$⊢y=x\to \left(\phi \to \psi \right)$$
Assertion	bj-cbvexivw	$$⊢\exists x\phi \to \exists y\psi$$

Proof

Step	Hyp	Ref	Expression
1		bj-cbvexivw.1	$$⊢y=x\to \left(\phi \to \psi \right)$$
2		ax5e	$$⊢\exists x\exists y\psi \to \exists y\psi$$
3		ax-5	$$⊢\phi \to \forall y\phi$$
4	2 3 1	bj-cbvexiw	$$⊢\exists x\phi \to \exists y\psi$$