Theorem dmeqi 4828

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 4827	. 2 |- ( A = B -> dom A = dom B )
3	1, 2	ax-mp 5	1 |- dom A = dom B

Syntax hints:   = wceq 1353   dom cdm 4626

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 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-3an 980  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2739  df-un 3133  df-in 3135  df-ss 3142  df-sn 3598  df-pr 3599  df-op 3601  df-br 4004  df-dm 4636

This theorem is referenced by:  dmxpm  4847  dmxpid  4848  dmxpin  4849  rncoss  4897  rncoeq  4900  rnun  5037  rnin  5038  rnxpm  5058  rnxpss  5060  imainrect  5074  dmpropg  5101  dmtpop  5104  rnsnopg  5107  fntpg  5272  fnreseql  5626  dmoprab  5955  reldmmpo  5985  elmpocl  6068  tfrlem8  6318  tfr2a  6321  tfrlemi14d  6333  tfr1onlemres  6349  tfri1dALT  6351  tfrcllemres  6362  xpassen  6829  sbthlemi5  6959  casedm  7084  djudm  7103  ctssdccl  7109  dmaddpi  7323  dmmulpi  7324  dmaddpq  7377  dmmulpq  7378  axaddf  7866  axmulf  7867  ennnfonelemom  12408  ennnfonelemdm  12420