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Theorem dmeqi 4459
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 4458 . 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 1226  dom cdm 4268
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 617  ax-5 1312  ax-7 1313  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-8 1372  ax-10 1373  ax-11 1374  ax-i12 1375  ax-bnd 1376  ax-4 1377  ax-17 1396  ax-i9 1400  ax-ial 1405  ax-i5r 1406  ax-ext 2000
This theorem depends on definitions:  df-bi 110  df-3an 873  df-tru 1229  df-nf 1326  df-sb 1624  df-clab 2005  df-cleq 2011  df-clel 2014  df-nfc 2145  df-v 2533  df-un 2895  df-in 2897  df-ss 2904  df-sn 3352  df-pr 3353  df-op 3355  df-br 3735  df-dm 4278
This theorem is referenced by:  dmxpm  4478  dmxpinm  4479  rncoss  4525  rncoeq  4528  rnun  4655  rnin  4656  rnxpm  4675  rnxpss  4677  imainrect  4689  dmpropg  4716  dmtpop  4719  rnsnopg  4722  fntpg  4877  fnreseql  5198  dmoprab  5504  reldmmpt2  5531  elmpt2cl  5617  tfrlem8  5852  tfr2a  5854  tfrlemi14d  5864  tfrlemi14  5865  dmaddpi  6179  dmmulpi  6180  dmaddpq  6232  dmmulpq  6233
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