Theorem rabbi2dva

Description: Deduction from a wff to a restricted class abstraction. (Contributed by NM, 14-Jan-2014)

	Ref	Expression
Hypothesis	rabbi2dva.1	|- ( ( ph /\ x e. A ) -> ( x e. B <-> ps ) )
Assertion	rabbi2dva	|- ( ph -> ( A i^i B ) = { x e. A | ps } )

Proof

Step	Hyp	Ref	Expression
1		rabbi2dva.1	|- ( ( ph /\ x e. A ) -> ( x e. B <-> ps ) )
2		dfin5	|- ( A i^i B ) = { x e. A | x e. B }
3	1	rabbidva	|- ( ph -> { x e. A | x e. B } = { x e. A | ps } )
4	2 3	eqtrid	|- ( ph -> ( A i^i B ) = { x e. A | ps } )