Theorem rexeqOLD

Description: Obsolete version of rexeq as of 5-May-2023. Equality theorem for restricted existential quantifier. (Contributed by NM, 29-Oct-1995) (New usage is discouraged.) (Proof modification is discouraged.)

	Ref	Expression
Assertion	rexeqOLD	$$⊢A=B\to \left(\exists x\in A\phi \leftrightarrow \exists x\in B\phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		nfcv	$$⊢\underset{\_}{Ⅎ}xA$$
2		nfcv	$$⊢\underset{\_}{Ⅎ}xB$$
3	1 2	rexeqf	$$⊢A=B\to \left(\exists x\in A\phi \leftrightarrow \exists x\in B\phi \right)$$