Theorem rabeqbidv

Description: Equality of restricted class abstractions. (Contributed by Jeff Madsen, 1-Dec-2009)

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

Proof

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