Theorem ceqsexgvOLD

Description: Obsolete version of ceqsexgv as of 1-Dec-2023. (Contributed by NM, 29-Dec-1996) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	ceqsexgv.1	$$⊢x=A\to \left(\phi \leftrightarrow \psi \right)$$
Assertion	ceqsexgvOLD	$$⊢A\in V\to \left(\exists x\left(x=A\wedge \phi \right)\leftrightarrow \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		ceqsexgv.1	$$⊢x=A\to \left(\phi \leftrightarrow \psi \right)$$
2		nfv	$$⊢Ⅎx\psi$$
3	2 1	ceqsexg	$$⊢A\in V\to \left(\exists x\left(x=A\wedge \phi \right)\leftrightarrow \psi \right)$$