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Theorem vpwex 4819
Description: The powerset of a setvar is a set. (Contributed by BJ, 3-May-2021.)
Assertion
Ref Expression
vpwex 𝒫 𝑥 ∈ V

Proof of Theorem vpwex
StepHypRef Expression
1 vex 3193 . 2 𝑥 ∈ V
21pwex 4818 1 𝒫 𝑥 ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 1987  Vcvv 3190  𝒫 cpw 4136
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601  ax-sep 4751  ax-pow 4813
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-v 3192  df-in 3567  df-ss 3574  df-pw 4138
This theorem is referenced by:  pwexg  4820  pwnex  6932  inf3lem7  8491  dfac8  8917  dfac13  8924  ackbij1lem5  9006  ackbij1lem8  9009  dominf  9227  numthcor  9276  dominfac  9355  intwun  9517  wunex2  9520  eltsk2g  9533  inttsk  9556  tskcard  9563  intgru  9596  gruina  9600  axgroth6  9610  ismre  16190  fnmre  16191  mreacs  16259  isacs5lem  17109  pmtrfval  17810  istopon  20657  dmtopon  20667  tgdom  20722  isfbas  21573  bj-snglex  32661  pwinfi  37389  ntrrn  37941  ntrf  37942  dssmapntrcls  37947
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