Theorem rabexg

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

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

Proof

Step	Hyp	Ref	Expression
1		ssrab2	⊢ { 𝑥 ∈ 𝐴 ∣ 𝜑 } ⊆ 𝐴
2		ssexg	⊢ ( ( { 𝑥 ∈ 𝐴 ∣ 𝜑 } ⊆ 𝐴 ∧ 𝐴 ∈ 𝑉 ) → { 𝑥 ∈ 𝐴 ∣ 𝜑 } ∈ V )
3	1 2	mpan	⊢ ( 𝐴 ∈ 𝑉 → { 𝑥 ∈ 𝐴 ∣ 𝜑 } ∈ V )