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Theorem rabexf 44285
Description: Separation Scheme in terms of a restricted class abstraction. (Contributed by Glauco Siliprandi, 23-Oct-2021.)
Hypotheses
Ref Expression
rabexf.1 𝑥𝐴
rabexf.2 𝐴𝑉
Assertion
Ref Expression
rabexf {𝑥𝐴𝜑} ∈ V

Proof of Theorem rabexf
StepHypRef Expression
1 rabexf.2 . 2 𝐴𝑉
2 rabexf.1 . . 3 𝑥𝐴
32rabexgf 44171 . 2 (𝐴𝑉 → {𝑥𝐴𝜑} ∈ V)
41, 3ax-mp 5 1 {𝑥𝐴𝜑} ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2105  wnfc 2882  {crab 3431  Vcvv 3473
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2153  ax-12 2170  ax-ext 2702  ax-sep 5299
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-tru 1543  df-ex 1781  df-nf 1785  df-sb 2067  df-clab 2709  df-cleq 2723  df-clel 2809  df-nfc 2884  df-rab 3432  df-v 3475  df-in 3955  df-ss 3965
This theorem is referenced by:  limsupequzmpt2  44893  liminfequzmpt2  44966  fsupdm  46017  finfdm  46021
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