Theorem dmeqi 4805

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 4804	. 2 |- ( A = B -> dom A = dom B )
3	1, 2	ax-mp 5	1 |- dom A = dom B

Syntax hints:   = wceq 1343   dom cdm 4604

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 699  ax-5 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-10 1493  ax-11 1494  ax-i12 1495  ax-bndl 1497  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-i5r 1523  ax-ext 2147

This theorem depends on definitions:  df-bi 116  df-3an 970  df-tru 1346  df-nf 1449  df-sb 1751  df-clab 2152  df-cleq 2158  df-clel 2161  df-nfc 2297  df-v 2728  df-un 3120  df-in 3122  df-ss 3129  df-sn 3582  df-pr 3583  df-op 3585  df-br 3983  df-dm 4614

This theorem is referenced by:  dmxpm  4824  dmxpid  4825  dmxpin  4826  rncoss  4874  rncoeq  4877  rnun  5012  rnin  5013  rnxpm  5033  rnxpss  5035  imainrect  5049  dmpropg  5076  dmtpop  5079  rnsnopg  5082  fntpg  5244  fnreseql  5595  dmoprab  5923  reldmmpo  5953  elmpocl  6036  tfrlem8  6286  tfr2a  6289  tfrlemi14d  6301  tfr1onlemres  6317  tfri1dALT  6319  tfrcllemres  6330  xpassen  6796  sbthlemi5  6926  casedm  7051  djudm  7070  ctssdccl  7076  dmaddpi  7266  dmmulpi  7267  dmaddpq  7320  dmmulpq  7321  axaddf  7809  axmulf  7810  ennnfonelemom  12341  ennnfonelemdm  12353