Theorem rabex

Description: Separation Scheme in terms of a restricted class abstraction. (Contributed by NM, 19-Jul-1996)

	Ref	Expression
Hypothesis	rabex.1	⊢ 𝐴 ∈ V
Assertion	rabex	⊢ { 𝑥 ∈ 𝐴 ∣ 𝜑 } ∈ V

Proof

Step	Hyp	Ref	Expression
1		rabex.1	⊢ 𝐴 ∈ V
2		rabexg	⊢ ( 𝐴 ∈ V → { 𝑥 ∈ 𝐴 ∣ 𝜑 } ∈ V )
3	1 2	ax-mp	⊢ { 𝑥 ∈ 𝐴 ∣ 𝜑 } ∈ V