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Theorem dmeqi 4824
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 4823 . 2  |-  ( A  =  B  ->  dom  A  =  dom  B )
31, 2ax-mp 5 1  |-  dom  A  =  dom  B
Colors of variables: wff set class
Syntax hints:    = wceq 1353   dom cdm 4623
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-3an 980  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2739  df-un 3133  df-in 3135  df-ss 3142  df-sn 3597  df-pr 3598  df-op 3600  df-br 4001  df-dm 4633
This theorem is referenced by:  dmxpm  4843  dmxpid  4844  dmxpin  4845  rncoss  4893  rncoeq  4896  rnun  5033  rnin  5034  rnxpm  5054  rnxpss  5056  imainrect  5070  dmpropg  5097  dmtpop  5100  rnsnopg  5103  fntpg  5268  fnreseql  5622  dmoprab  5950  reldmmpo  5980  elmpocl  6063  tfrlem8  6313  tfr2a  6316  tfrlemi14d  6328  tfr1onlemres  6344  tfri1dALT  6346  tfrcllemres  6357  xpassen  6824  sbthlemi5  6954  casedm  7079  djudm  7098  ctssdccl  7104  dmaddpi  7315  dmmulpi  7316  dmaddpq  7369  dmmulpq  7370  axaddf  7858  axmulf  7859  ennnfonelemom  12392  ennnfonelemdm  12404
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