Theorem rexeqtrrdv

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

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

Proof

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