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Theorem dmeqi 4479
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 4478 . 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 1242  dom cdm 4288
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-un 2916  df-in 2918  df-ss 2925  df-sn 3373  df-pr 3374  df-op 3376  df-br 3756  df-dm 4298
This theorem is referenced by:  dmxpm  4498  dmxpinm  4499  rncoss  4545  rncoeq  4548  rnun  4675  rnin  4676  rnxpm  4695  rnxpss  4697  imainrect  4709  dmpropg  4736  dmtpop  4739  rnsnopg  4742  fntpg  4898  fnreseql  5220  dmoprab  5527  reldmmpt2  5554  elmpt2cl  5640  tfrlem8  5875  tfr2a  5877  tfrlemi14d  5888  xpassen  6240  dmaddpi  6309  dmmulpi  6310  dmaddpq  6363  dmmulpq  6364
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