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Theorem dmeqi 5038
Description: Equality inference for domain. (Contributed by NM, 4-Mar-2004.)
Hypothesis
Ref Expression
dmeqi.1  |-  A  =  B
Assertion
Ref Expression
dmeqi  |-  dom  A  =  dom  B

Proof of Theorem dmeqi
StepHypRef Expression
1 dmeqi.1 . 2  |-  A  =  B
2 dmeq 5037 . 2  |-  ( A  =  B  ->  dom  A  =  dom  B )
31, 2ax-mp 8 1  |-  dom  A  =  dom  B
Colors of variables: wff set class
Syntax hints:    = wceq 1649   dom cdm 4845
This theorem is referenced by:  dmxp  5055  dmxpin  5057  rncoss  5103  rncoeq  5106  rnun  5247  rnin  5248  rnxp  5266  rnxpss  5268  imainrect  5279  dmpropg  5310  dmtpop  5313  rnsnopg  5316  fntpg  5473  dffv2  5763  fvopab4ndm  5792  fnreseql  5807  dmoprab  6121  reldmmpt2  6148  elmpt2cl  6255  bropopvvv  6393  mpt2ndm0  6440  opabiotadm  6504  tfrlem8  6612  tfr1a  6622  tfr2a  6623  tfr2b  6624  rdgseg  6647  xpassen  7169  sbthlem5  7188  hartogslem1  7475  r1funlim  7656  r1sucg  7659  r1limg  7661  rankf  7684  hsmexlem4  8273  axdc2lem  8292  dmaddpi  8731  dmmulpi  8732  dmaddsr  8924  dmmulsr  8925  axaddf  8984  axmulf  8985  strlemor1  13519  divsfval  13735  xpsfrnel2  13753  ismbl  19383  volres  19385  efcvx  20326  dvrelog  20489  dvlog  20503  usgrares1  21385  usgrafilem1  21386  cusgrasizeindslem2  21444  wlkntrllem1  21520  eupares  21658  resgrprn  21829  ismgm  21869  dfhnorm2  22585  hlimcaui  22700  hhshsslem1  22728  dmadjss  23351  adjeu  23353  adj1o  23358  mbfmcst  24570  0rrv  24670  coinflipspace  24699  ghomfo  25063  wfrlem7  25484  wfrlem9  25486  wfrlem16  25493  frrlem7  25513  nofulllem5  25582  fixun  25671  linedegen  25989  ssbnd  26395  exidreslem  26450  dmmzp  26688  mvdco  27264  symgsssg  27284  symgfisg  27285  psgnunilem5  27293  dvsid  27424  dvsef  27425  stoweidlem27  27651  2wlkonot3v  28080  2spthonot3v  28081  bnj96  28954  bnj1398  29121  bnj1416  29126  bnj1450  29137  bnj1498  29148  bnj1501  29154
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2393
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2399  df-cleq 2405  df-clel 2408  df-nfc 2537  df-rab 2683  df-v 2926  df-dif 3291  df-un 3293  df-in 3295  df-ss 3302  df-nul 3597  df-if 3708  df-sn 3788  df-pr 3789  df-op 3791  df-br 4181  df-dm 4855
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