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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 1259  dom cdm 4373
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-3an 898  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-un 2950  df-in 2952  df-ss 2959  df-sn 3409  df-pr 3410  df-op 3412  df-br 3793  df-dm 4383
This theorem is referenced by:  dmxpm  4583  dmxpinm  4584  rncoss  4630  rncoeq  4633  rnun  4760  rnin  4761  rnxpm  4780  rnxpss  4782  imainrect  4794  dmpropg  4821  dmtpop  4824  rnsnopg  4827  fntpg  4983  fnreseql  5305  dmoprab  5613  reldmmpt2  5640  elmpt2cl  5726  tfrlem8  5965  tfr2a  5967  tfrlemi14d  5978  xpassen  6335  dmaddpi  6481  dmmulpi  6482  dmaddpq  6535  dmmulpq  6536
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