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Theorem eluni 3553
Description: Membership in class union. (Contributed by NM, 22-May-1994.)
Assertion
Ref Expression
eluni  U.
Distinct variable groups:   ,   ,

Proof of Theorem eluni
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 elex 2539 . 2  U.  _V
2 elex 2539 . . . 4  _V
32adantr 261 . . 3  _V
43exlimiv 1467 . 2  _V
5 eleq1 2078 . . . . 5
65anbi1d 441 . . . 4
76exbidv 1684 . . 3
8 df-uni 3551 . . 3  U.  {  |  }
97, 8elab2g 2662 . 2  _V  U.
101, 4, 9pm5.21nii 607 1  U.
Colors of variables: wff set class
Syntax hints:   wa 97   wb 98   wceq 1226  wex 1358   wcel 1370   _Vcvv 2531   U.cuni 3550
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 617  ax-5 1312  ax-7 1313  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-8 1372  ax-10 1373  ax-11 1374  ax-i12 1375  ax-bnd 1376  ax-4 1377  ax-17 1396  ax-i9 1400  ax-ial 1405  ax-i5r 1406  ax-ext 2000
This theorem depends on definitions:  df-bi 110  df-tru 1229  df-nf 1326  df-sb 1624  df-clab 2005  df-cleq 2011  df-clel 2014  df-nfc 2145  df-v 2533  df-uni 3551
This theorem is referenced by:  eluni2  3554  elunii  3555  eluniab  3562  uniun  3569  uniin  3570  uniss  3571  unissb  3580  dftr2  3826  unidif0  3890  unipw  3923  uniex2  4119  uniuni  4129  limom  4259  dmuni  4468  fununi  4889  nfvres  5127  elunirn  5326  tfrlem7  5851  tfrexlem  5866  bj-uniex2  7331
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