Theorem ssab

Description: Subclass of a class abstraction. (Contributed by NM, 16-Aug-2006)

	Ref	Expression
Assertion	ssab	|- ( A C_ { x | ph } <-> A. x ( x e. A -> ph ) )

Proof

Step	Hyp	Ref	Expression
1		abid2	|- { x | x e. A } = A
2	1	sseq1i	|- ( { x | x e. A } C_ { x | ph } <-> A C_ { x | ph } )
3		ss2ab	|- ( { x | x e. A } C_ { x | ph } <-> A. x ( x e. A -> ph ) )
4	2 3	bitr3i	|- ( A C_ { x | ph } <-> A. x ( x e. A -> ph ) )