Theorem dmeqi 4554

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

Step	Hyp	Ref	Expression
1		dmeqi.1	. 2 |- A = B
2		dmeq 4553	. 2 |- ( A = B -> dom A = dom B )
3	1, 2	ax-mp 7	1 |- dom A = dom B

Syntax hints:   = wceq 1284   dom cdm 4363

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 662  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-10 1436  ax-11 1437  ax-i12 1438  ax-bndl 1439  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-3an 921  df-tru 1287  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-nfc 2208  df-v 2603  df-un 2977  df-in 2979  df-ss 2986  df-sn 3404  df-pr 3405  df-op 3407  df-br 3786  df-dm 4373

This theorem is referenced by:  dmxpm  4573  dmxpinm  4574  rncoss  4620  rncoeq  4623  rnun  4752  rnin  4753  rnxpm  4772  rnxpss  4774  imainrect  4786  dmpropg  4813  dmtpop  4816  rnsnopg  4819  fntpg  4975  fnreseql  5298  dmoprab  5605  reldmmpt2  5632  elmpt2cl  5718  tfrlem8  5957  tfr2a  5959  tfrlemi14d  5970  xpassen  6327  dmaddpi  6515  dmmulpi  6516  dmaddpq  6569  dmmulpq  6570