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Theorem dmeqi 4708
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 4707 . 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 1314  dom cdm 4507
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 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-3an 947  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-v 2660  df-un 3043  df-in 3045  df-ss 3052  df-sn 3501  df-pr 3502  df-op 3504  df-br 3898  df-dm 4517
This theorem is referenced by:  dmxpm  4727  dmxpid  4728  dmxpin  4729  rncoss  4777  rncoeq  4780  rnun  4915  rnin  4916  rnxpm  4936  rnxpss  4938  imainrect  4952  dmpropg  4979  dmtpop  4982  rnsnopg  4985  fntpg  5147  fnreseql  5496  dmoprab  5818  reldmmpo  5848  elmpocl  5934  tfrlem8  6181  tfr2a  6184  tfrlemi14d  6196  tfr1onlemres  6212  tfri1dALT  6214  tfrcllemres  6225  xpassen  6690  sbthlemi5  6815  casedm  6937  djudm  6956  ctssdccl  6962  dmaddpi  7097  dmmulpi  7098  dmaddpq  7151  dmmulpq  7152  axaddf  7640  axmulf  7641  ennnfonelemom  11827  ennnfonelemdm  11839
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