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Theorem dmex 5124
Description: The domain of a set is a set. Corollary 6.8(2) of [TakeutiZaring] p. 26. (Contributed by NM, 7-Jul-2008.)
Hypothesis
Ref Expression
dmex.1  |-  A  e. 
_V
Assertion
Ref Expression
dmex  |-  dom  A  e.  _V

Proof of Theorem dmex
StepHypRef Expression
1 dmex.1 . 2  |-  A  e. 
_V
2 dmexg 5122 . 2  |-  ( A  e.  _V  ->  dom  A  e.  _V )
31, 2ax-mp 8 1  |-  dom  A  e.  _V
Colors of variables: wff set class
Syntax hints:    e. wcel 1725   _Vcvv 2948   dom cdm 4870
This theorem is referenced by:  elxp4  5349  ofmres  6335  1stval  6343  fo1st  6358  frxp  6448  tfrlem8  6637  mapprc  7014  ixpprc  7075  bren  7109  brdomg  7110  fundmen  7172  domssex  7260  mapen  7263  ssenen  7273  hartogslem1  7503  brwdomn0  7529  unxpwdom2  7548  ixpiunwdom  7551  oemapwe  7642  cantnffval2  7643  r0weon  7886  fseqenlem2  7898  acndom  7924  acndom2  7927  dfac9  8008  ackbij2lem2  8112  ackbij2lem3  8113  cfsmolem  8142  coftr  8145  dcomex  8319  axdc3lem4  8325  axdclem  8391  axdclem2  8392  fodomb  8396  brdom3  8398  brdom5  8399  brdom4  8400  hashfacen  11695  shftfval  11877  prdsval  13670  isoval  13982  issubc  14027  prfval  14288  symgbas  15087  dfac14  17642  indishmph  17822  ufldom  17986  tsmsval2  18151  dvmptadd  19838  dvmptmul  19839  dvmptco  19850  taylfval  20267  hmoval  22303  ctex  24092  sitmval  24653  dfrdg4  25787  tfrqfree  25788  indexdom  26427  aomclem1  27120  dfac21  27132  psgnghm2  27406  bnj893  29236  dibfval  31876
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395  ax-un 4693
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-opab 4259  df-cnv 4878  df-dm 4880  df-rn 4881
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