Theorem rabexd

Description: Separation Scheme in terms of a restricted class abstraction, deduction form of rabex2 . (Contributed by AV, 16-Jul-2019)

	Ref	Expression
Hypotheses	rabexd.1	$$⊢B=\left\{x\in A|\psi \right\}$$
	rabexd.2	$$⊢\phi \to A\in V$$
Assertion	rabexd	$$⊢\phi \to B\in \mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		rabexd.1	$$⊢B=\left\{x\in A|\psi \right\}$$
2		rabexd.2	$$⊢\phi \to A\in V$$
3		rabexg	$$⊢A\in V\to \left\{x\in A|\psi \right\}\in \mathrm{V}$$
4	2 3	syl	$$⊢\phi \to \left\{x\in A|\psi \right\}\in \mathrm{V}$$
5	1 4	eqeltrid	$$⊢\phi \to B\in \mathrm{V}$$