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Metamath Proof Explorer

Theorem rabex2

Description: Separation Scheme in terms of a restricted class abstraction. (Contributed by AV, 16-Jul-2019) (Revised by AV, 26-Mar-2021)

Ref Expression
Hypotheses rabex2.1 ⊢ 𝐵 = { 𝑥 ∈ 𝐴 ∣ 𝜓 }
rabex2.2 ⊢ 𝐴 ∈ V
Assertion rabex2 𝐵 ∈ V

Proof

Step Hyp Ref Expression
1 rabex2.1 ⊢ 𝐵 = { 𝑥 ∈ 𝐴 ∣ 𝜓 }
2 rabex2.2 ⊢ 𝐴 ∈ V
3 id ⊢ ( 𝐴 ∈ V → 𝐴 ∈ V )
4 1 3 rabexd ⊢ ( 𝐴 ∈ V → 𝐵 ∈ V )
5 2 4 ax-mp ⊢ 𝐵 ∈ V