Theorem dmeqi 4846

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 4845	. 2 |- ( A = B -> dom A = dom B )
3	1, 2	ax-mp 5	1 |- dom A = dom B

Syntax hints:   = wceq 1364   dom cdm 4644

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171

This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-v 2754  df-un 3148  df-in 3150  df-ss 3157  df-sn 3613  df-pr 3614  df-op 3616  df-br 4019  df-dm 4654

This theorem is referenced by:  dmxpm  4865  dmxpid  4866  dmxpin  4867  rncoss  4915  rncoeq  4918  rnun  5055  rnin  5056  rnxpm  5076  rnxpss  5078  imainrect  5092  dmpropg  5119  dmtpop  5122  rnsnopg  5125  fntpg  5291  fnreseql  5647  dmoprab  5978  reldmmpo  6009  elmpocl  6092  tfrlem8  6344  tfr2a  6347  tfrlemi14d  6359  tfr1onlemres  6375  tfri1dALT  6377  tfrcllemres  6388  xpassen  6857  sbthlemi5  6991  casedm  7116  djudm  7135  ctssdccl  7141  dmaddpi  7355  dmmulpi  7356  dmaddpq  7409  dmmulpq  7410  axaddf  7898  axmulf  7899  ennnfonelemom  12462  ennnfonelemdm  12474