Theorem ssabral

Description: The relation for a subclass of a class abstraction is equivalent to restricted quantification. (Contributed by NM, 6-Sep-2006)

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

Proof

Step	Hyp	Ref	Expression
1		ssab	|- ( A C_ { x | ph } <-> A. x ( x e. A -> ph ) )
2		df-ral	|- ( A. x e. A ph <-> A. x ( x e. A -> ph ) )
3	1 2	bitr4i	|- ( A C_ { x | ph } <-> A. x e. A ph )