Theorem dmeqi 4880

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 4879	. 2 |- ( A = B -> dom A = dom B )
3	1, 2	ax-mp 5	1 |- dom A = dom B

Syntax hints:   = wceq 1373   dom cdm 4676

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 711  ax-5 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-bndl 1532  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-3an 983  df-tru 1376  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-nfc 2337  df-v 2774  df-un 3170  df-in 3172  df-ss 3179  df-sn 3639  df-pr 3640  df-op 3642  df-br 4046  df-dm 4686

This theorem is referenced by:  dmxpm  4899  dmxpid  4900  dmxpin  4901  rncoss  4950  rncoeq  4953  rnun  5092  rnin  5093  rnxpm  5113  rnxpss  5115  imainrect  5129  dmpropg  5156  dmtpop  5159  rnsnopg  5162  fntpg  5331  fnreseql  5692  dmoprab  6028  reldmmpo  6059  elmpocl  6143  tfrlem8  6406  tfr2a  6409  tfrlemi14d  6421  tfr1onlemres  6437  tfri1dALT  6439  tfrcllemres  6450  xpassen  6927  sbthlemi5  7065  casedm  7190  djudm  7209  ctssdccl  7215  dmaddpi  7440  dmmulpi  7441  dmaddpq  7494  dmmulpq  7495  axaddf  7983  axmulf  7984  ennnfonelemom  12812  ennnfonelemdm  12824  structiedg0val  15670