Theorem rabexg

Description: Separation Scheme in terms of a restricted class abstraction. (Contributed by NM, 23-Oct-1999) (Proof shortened by BJ, 24-Jul-2025)

	Ref	Expression
Assertion	rabexg	⊢ ( 𝐴 ∈ 𝑉 → { 𝑥 ∈ 𝐴 ∣ 𝜑 } ∈ V )

Proof

Step	Hyp	Ref	Expression
1		rabelpw	⊢ ( 𝐴 ∈ 𝑉 → { 𝑥 ∈ 𝐴 ∣ 𝜑 } ∈ 𝒫 𝐴 )
2	1	elexd	⊢ ( 𝐴 ∈ 𝑉 → { 𝑥 ∈ 𝐴 ∣ 𝜑 } ∈ V )