Theorem rabelpw

Description: A restricted class abstraction is an element of the power set of its restricting set. (Contributed by AV, 9-Oct-2023)

	Ref	Expression
Assertion	rabelpw	|- ( A e. V -> { x e. A | ph } e. ~P A )

Proof

Step	Hyp	Ref	Expression
1		ssrab2	|- { x e. A | ph } C_ A
2		elpw2g	|- ( A e. V -> ( { x e. A | ph } e. ~P A <-> { x e. A | ph } C_ A ) )
3	1 2	mpbiri	|- ( A e. V -> { x e. A | ph } e. ~P A )