Theorem rexeqtrdv

Description: Substitution of equal classes into a restricted existential quantifier. (Contributed by Matthew House, 21-Jul-2025)

	Ref	Expression
Hypotheses	rexeqtrdv.1	|- ( ph -> E. x e. A ps )
	rexeqtrdv.2	|- ( ph -> A = B )
Assertion	rexeqtrdv	|- ( ph -> E. x e. B ps )

Proof

Step	Hyp	Ref	Expression
1		rexeqtrdv.1	|- ( ph -> E. x e. A ps )
2		rexeqtrdv.2	|- ( ph -> A = B )
3	2	rexeqdv	|- ( ph -> ( E. x e. A ps <-> E. x e. B ps ) )
4	1 3	mpbid	|- ( ph -> E. x e. B ps )