Metamath Proof Explorer


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