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Metamath Proof Explorer

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