Theorem rabexf

Description: Separation Scheme in terms of a restricted class abstraction. (Contributed by Glauco Siliprandi, 23-Oct-2021)

	Ref	Expression
Hypotheses	rabexf.1	$$⊢\underset{\_}{Ⅎ}xA$$
	rabexf.2	$$⊢A\in V$$
Assertion	rabexf	$$⊢\left\{x\in A|\phi \right\}\in \mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		rabexf.1	$$⊢\underset{\_}{Ⅎ}xA$$
2		rabexf.2	$$⊢A\in V$$
3	1	rabexgf	$$⊢A\in V\to \left\{x\in A|\phi \right\}\in \mathrm{V}$$
4	2 3	ax-mp	$$⊢\left\{x\in A|\phi \right\}\in \mathrm{V}$$