Theorem sepab

Description: Separation Scheme (Aussonderung) in terms of a class abstraction. Prefer using the more natural statement rabexg . (Contributed by NM, 8-Jun-1994) Put in closed form. (Revised by BJ, 18-Jul-2026)

	Ref	Expression
Assertion	sepab	|- ( A e. V -> { x | ( x e. A /\ ph ) } e. _V )

Proof

Step	Hyp	Ref	Expression
1		id	|- ( A e. V -> A e. V )
2		ssab2	|- { x | ( x e. A /\ ph ) } C_ A
3	2	a1i	|- ( A e. V -> { x | ( x e. A /\ ph ) } C_ A )
4	1 3	ssexd	|- ( A e. V -> { x | ( x e. A /\ ph ) } e. _V )