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	1	rabeqdv	|- ( ph -> { x e. A | ps } = { x e. B | ps } )
4	2	rabbidv	|- ( ph -> { x e. B | ps } = { x e. B | ch } )
5	3 4	eqtrd	|- ( ph -> { x e. A | ps } = { x e. B | ch } )