Theorem dmeqi 4829

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 4828	. 2 |- ( A = B -> dom A = dom B )
3	1, 2	ax-mp 5	1 |- dom A = dom B

Syntax hints:   = wceq 1353   dom cdm 4627

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 2740  df-un 3134  df-in 3136  df-ss 3143  df-sn 3599  df-pr 3600  df-op 3602  df-br 4005  df-dm 4637

This theorem is referenced by:  dmxpm  4848  dmxpid  4849  dmxpin  4850  rncoss  4898  rncoeq  4901  rnun  5038  rnin  5039  rnxpm  5059  rnxpss  5061  imainrect  5075  dmpropg  5102  dmtpop  5105  rnsnopg  5108  fntpg  5273  fnreseql  5627  dmoprab  5956  reldmmpo  5986  elmpocl  6069  tfrlem8  6319  tfr2a  6322  tfrlemi14d  6334  tfr1onlemres  6350  tfri1dALT  6352  tfrcllemres  6363  xpassen  6830  sbthlemi5  6960  casedm  7085  djudm  7104  ctssdccl  7110  dmaddpi  7324  dmmulpi  7325  dmaddpq  7378  dmmulpq  7379  axaddf  7867  axmulf  7868  ennnfonelemom  12409  ennnfonelemdm  12421