Theorem cbvexvOLD

Description: Obsolete version of cbvexv as of 11-Sep-2023. (Contributed by NM, 21-Jun-1993) Remove dependency on ax-10 . (Revised by Wolf Lammen, 17-Jul-2021) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	cbvalv.1	$$⊢x=y\to \left(\phi \leftrightarrow \psi \right)$$
Assertion	cbvexvOLD	$$⊢\exists x\phi \leftrightarrow \exists y\psi$$

Proof

Step	Hyp	Ref	Expression
1		cbvalv.1	$$⊢x=y\to \left(\phi \leftrightarrow \psi \right)$$
2	1	notbid	$$⊢x=y\to \left(\neg \phi \leftrightarrow \neg \psi \right)$$
3	2	cbvalv	$$⊢\forall x\neg \phi \leftrightarrow \forall y\neg \psi$$
4		alnex	$$⊢\forall x\neg \phi \leftrightarrow \neg \exists x\phi$$
5		alnex	$$⊢\forall y\neg \psi \leftrightarrow \neg \exists y\psi$$
6	3 4 5	3bitr3i	$$⊢\neg \exists x\phi \leftrightarrow \neg \exists y\psi$$
7	6	con4bii	$$⊢\exists x\phi \leftrightarrow \exists y\psi$$