Theorem rabexf

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

	Ref	Expression
Hypotheses	rabexf.1	⊢ Ⅎ 𝑥 𝐴
	rabexf.2	⊢ 𝐴 ∈ 𝑉
Assertion	rabexf	⊢ { 𝑥 ∈ 𝐴 ∣ 𝜑 } ∈ V

Proof

Step	Hyp	Ref	Expression
1		rabexf.1	⊢ Ⅎ 𝑥 𝐴
2		rabexf.2	⊢ 𝐴 ∈ 𝑉
3	1	rabexgf	⊢ ( 𝐴 ∈ 𝑉 → { 𝑥 ∈ 𝐴 ∣ 𝜑 } ∈ V )
4	2 3	ax-mp	⊢ { 𝑥 ∈ 𝐴 ∣ 𝜑 } ∈ V