Theorem ssabf

Description: Subclass of a class abstraction. (Contributed by Glauco Siliprandi, 26-Jun-2021)

	Ref	Expression
Hypothesis	ssabf.1	|- F/_ x A
Assertion	ssabf	|- ( A C_ { x | ph } <-> A. x ( x e. A -> ph ) )

Proof

Step	Hyp	Ref	Expression
1		ssabf.1	|- F/_ x A
2	1	abid2f	|- { x | x e. A } = A
3	2	sseq1i	|- ( { x | x e. A } C_ { x | ph } <-> A C_ { x | ph } )
4		ss2ab	|- ( { x | x e. A } C_ { x | ph } <-> A. x ( x e. A -> ph ) )
5	3 4	bitr3i	|- ( A C_ { x | ph } <-> A. x ( x e. A -> ph ) )