Theorem raleqbidvv

Description: Version of raleqbidv with additional disjoint variable conditions, not requiring ax-8 nor df-clel . (Contributed by BJ, 22-Sep-2024)

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

Proof

Step	Hyp	Ref	Expression
1		raleqbidvv.1	|- ( ph -> A = B )
2		raleqbidvv.2	|- ( ph -> ( ps <-> ch ) )
3	2	adantr	|- ( ( ph /\ x e. A ) -> ( ps <-> ch ) )
4	1 3	raleqbidva	|- ( ph -> ( A. x e. A ps <-> A. x e. B ch ) )