Theorem dmeqi 4825

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 4824	. 2 |- ( A = B -> dom A = dom B )
3	1, 2	ax-mp 5	1 |- dom A = dom B

Syntax hints:   = wceq 1353   dom cdm 4624

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 4002  df-dm 4634

This theorem is referenced by:  dmxpm  4844  dmxpid  4845  dmxpin  4846  rncoss  4894  rncoeq  4897  rnun  5034  rnin  5035  rnxpm  5055  rnxpss  5057  imainrect  5071  dmpropg  5098  dmtpop  5101  rnsnopg  5104  fntpg  5269  fnreseql  5623  dmoprab  5951  reldmmpo  5981  elmpocl  6064  tfrlem8  6314  tfr2a  6317  tfrlemi14d  6329  tfr1onlemres  6345  tfri1dALT  6347  tfrcllemres  6358  xpassen  6825  sbthlemi5  6955  casedm  7080  djudm  7099  ctssdccl  7105  dmaddpi  7319  dmmulpi  7320  dmaddpq  7373  dmmulpq  7374  axaddf  7862  axmulf  7863  ennnfonelemom  12399  ennnfonelemdm  12411