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Theorem rabexf 39840
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 39705 . 2 (𝐴𝑉 → {𝑥𝐴𝜑} ∈ V)
41, 3ax-mp 5 1 {𝑥𝐴𝜑} ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2145  wnfc 2900  {crab 3065  Vcvv 3351
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-9 2154  ax-10 2174  ax-11 2190  ax-12 2203  ax-13 2408  ax-ext 2751  ax-sep 4915
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 837  df-tru 1634  df-ex 1853  df-nf 1858  df-sb 2050  df-clab 2758  df-cleq 2764  df-clel 2767  df-nfc 2902  df-rab 3070  df-v 3353  df-in 3730  df-ss 3737
This theorem is referenced by:  limsupequzmpt2  40468  liminfequzmpt2  40541
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