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Theorem dmeqi 4812
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 4811 . 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 1348   dom cdm 4611
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-3an 975  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-v 2732  df-un 3125  df-in 3127  df-ss 3134  df-sn 3589  df-pr 3590  df-op 3592  df-br 3990  df-dm 4621
This theorem is referenced by:  dmxpm  4831  dmxpid  4832  dmxpin  4833  rncoss  4881  rncoeq  4884  rnun  5019  rnin  5020  rnxpm  5040  rnxpss  5042  imainrect  5056  dmpropg  5083  dmtpop  5086  rnsnopg  5089  fntpg  5254  fnreseql  5606  dmoprab  5934  reldmmpo  5964  elmpocl  6047  tfrlem8  6297  tfr2a  6300  tfrlemi14d  6312  tfr1onlemres  6328  tfri1dALT  6330  tfrcllemres  6341  xpassen  6808  sbthlemi5  6938  casedm  7063  djudm  7082  ctssdccl  7088  dmaddpi  7287  dmmulpi  7288  dmaddpq  7341  dmmulpq  7342  axaddf  7830  axmulf  7831  ennnfonelemom  12363  ennnfonelemdm  12375
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