Theorem raleqtrrdv

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

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

Proof

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