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Theorem rabexf 45074
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 44962 . 2 (𝐴𝑉 → {𝑥𝐴𝜑} ∈ V)
41, 3ax-mp 5 1 {𝑥𝐴𝜑} ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2106  wnfc 2888  {crab 3433  Vcvv 3478
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-10 2139  ax-11 2155  ax-12 2175  ax-ext 2706  ax-sep 5302
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1540  df-ex 1777  df-nf 1781  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-nfc 2890  df-rab 3434  df-v 3480  df-in 3970  df-ss 3980
This theorem is referenced by:  limsupequzmpt2  45674  liminfequzmpt2  45747  fsupdm  46798  finfdm  46802
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