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Theorem dmex 6516
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 6514 . 2  |-  ( A  e.  _V  ->  dom  A  e.  _V )
31, 2ax-mp 5 1  |-  dom  A  e.  _V
Colors of variables: wff setvar class
Syntax hints:    e. wcel 1756   _Vcvv 2977   dom cdm 4845
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-8 1758  ax-9 1760  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2423  ax-sep 4418  ax-nul 4426  ax-pr 4536  ax-un 6377
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-eu 2257  df-mo 2258  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2573  df-ne 2613  df-rex 2726  df-rab 2729  df-v 2979  df-dif 3336  df-un 3338  df-in 3340  df-ss 3347  df-nul 3643  df-if 3797  df-sn 3883  df-pr 3885  df-op 3889  df-uni 4097  df-br 4298  df-opab 4356  df-cnv 4853  df-dm 4855  df-rn 4856
This theorem is referenced by:  elxp4  6527  ofmres  6578  1stval  6584  fo1st  6601  frxp  6687  tfrlem8  6848  mapprc  7223  ixpprc  7289  bren  7324  brdomg  7325  fundmen  7388  domssex  7477  mapen  7480  ssenen  7490  hartogslem1  7761  brwdomn0  7789  unxpwdom2  7808  ixpiunwdom  7811  oemapwe  7907  cantnffval2  7908  oemapweOLD  7929  cantnffval2OLD  7930  r0weon  8184  fseqenlem2  8200  acndom  8226  acndom2  8229  dfac9  8310  ackbij2lem2  8414  ackbij2lem3  8415  cfsmolem  8444  coftr  8447  dcomex  8621  axdc3lem4  8627  axdclem  8693  axdclem2  8694  fodomb  8698  brdom3  8700  brdom5  8701  brdom4  8702  hashfacen  12212  shftfval  12564  prdsval  14398  isoval  14708  issubc  14753  prfval  15014  symgbas  15890  psgnghm2  18016  dfac14  19196  indishmph  19376  ufldom  19540  tsmsval2  19705  dvmptadd  21439  dvmptmul  21440  dvmptco  21451  taylfval  21829  hmoval  24215  ctex  26013  sitmval  26739  dfrdg4  27986  tfrqfree  27987  indexdom  28633  aomclem1  29412  dfac21  29424  bnj893  31926  dibfval  34791
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