Theorem ceqsexvOLD

Description: Obsolete version of ceqsexv as of 12-Oct-2024. (Contributed by NM, 2-Mar-1995) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ceqsexvOLD.1	$$⊢A\in \mathrm{V}$$
	ceqsexvOLD.2	$$⊢x=A\to \left(\phi \leftrightarrow \psi \right)$$
Assertion	ceqsexvOLD	$$⊢\exists x\left(x=A\wedge \phi \right)\leftrightarrow \psi$$

Proof

Step	Hyp	Ref	Expression
1		ceqsexvOLD.1	$$⊢A\in \mathrm{V}$$
2		ceqsexvOLD.2	$$⊢x=A\to \left(\phi \leftrightarrow \psi \right)$$
3		nfv	$$⊢Ⅎx\psi$$
4	3 1 2	ceqsex	$$⊢\exists x\left(x=A\wedge \phi \right)\leftrightarrow \psi$$