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	$$⊢A\in V\to \left\{x|\left(x\in A\wedge \phi \right)\right\}\in \mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		id	$$⊢A\in V\to A\in V$$
2		ssab2	$$⊢\left\{x|\left(x\in A\wedge \phi \right)\right\}\subseteq A$$
3	2	a1i	$$⊢A\in V\to \left\{x|\left(x\in A\wedge \phi \right)\right\}\subseteq A$$
4	1 3	ssexd	$$⊢A\in V\to \left\{x|\left(x\in A\wedge \phi \right)\right\}\in \mathrm{V}$$