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Theorem dmeqi 4564
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 4563 . 2  |-  ( A  =  B  ->  dom  A  =  dom  B )
31, 2ax-mp 7 1  |-  dom  A  =  dom  B
Colors of variables: wff set class
Syntax hints:    = wceq 1285   dom cdm 4371
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-un 2978  df-in 2980  df-ss 2987  df-sn 3412  df-pr 3413  df-op 3415  df-br 3794  df-dm 4381
This theorem is referenced by:  dmxpm  4583  dmxpinm  4584  rncoss  4630  rncoeq  4633  rnun  4762  rnin  4763  rnxpm  4782  rnxpss  4784  imainrect  4796  dmpropg  4823  dmtpop  4826  rnsnopg  4829  fntpg  4986  fnreseql  5309  dmoprab  5616  reldmmpt2  5643  elmpt2cl  5729  tfrlem8  5967  tfr2a  5970  tfrlemi14d  5982  tfr1onlemres  5998  tfri1dALT  6000  tfrcllemres  6011  xpassen  6374  dmaddpi  6577  dmmulpi  6578  dmaddpq  6631  dmmulpq  6632
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