Theorem rabexg

Description: Separation Scheme in terms of a restricted class abstraction. (Contributed by NM, 23-Oct-1999)

	Ref	Expression
Assertion	rabexg	$$⊢A\in V\to \left\{x\in A|\phi \right\}\in \mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		ssrab2	$$⊢\left\{x\in A|\phi \right\}\subseteq A$$
2		ssexg	$$⊢\left(\left\{x\in A|\phi \right\}\subseteq A\wedge A\in V\right)\to \left\{x\in A|\phi \right\}\in \mathrm{V}$$
3	1 2	mpan	$$⊢A\in V\to \left\{x\in A|\phi \right\}\in \mathrm{V}$$