MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  vuniex Structured version   Visualization version   GIF version

Theorem vuniex 6996
Description: The union of a setvar is a set. (Contributed by BJ, 3-May-2021.)
Assertion
Ref Expression
vuniex 𝑥 ∈ V

Proof of Theorem vuniex
StepHypRef Expression
1 vex 3234 . 2 𝑥 ∈ V
21uniex 6995 1 𝑥 ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2030  Vcvv 3231   cuni 4468
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-8 2032  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631  ax-sep 4814  ax-un 6991
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-rex 2947  df-v 3233  df-uni 4469
This theorem is referenced by:  uniexg  6997  uniuni  7013  rankuni  8764  r0weon  8873  dfac3  8982  dfac5lem4  8987  dfac8  8995  dfacacn  9001  kmlem2  9011  cfslb2n  9128  ttukeylem5  9373  ttukeylem6  9374  brdom7disj  9391  brdom6disj  9392  intwun  9595  wunex2  9598  fnmrc  16314  mrcfval  16315  mrisval  16337  sylow2a  18080  toprntopon  20777  distop  20847  fctop  20856  cctop  20858  ppttop  20859  epttop  20861  fncld  20874  mretopd  20944  toponmre  20945  iscnp2  21091  2ndcsep  21310  kgenf  21392  alexsubALTlem2  21899  pwsiga  30321  sigainb  30327  dmsigagen  30335  pwldsys  30348  ldsysgenld  30351  ldgenpisyslem1  30354  ddemeas  30427  brapply  32170  dfrdg4  32183  fnessref  32477  neibastop1  32479  finxpreclem2  33357  mbfresfi  33586  pwinfi  38186  pwsal  40853  intsal  40866  salexct  40870  0ome  41064
  Copyright terms: Public domain W3C validator