Theorem dmeqi 4868

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 4867	. 2 |- ( A = B -> dom A = dom B )
3	1, 2	ax-mp 5	1 |- dom A = dom B

Syntax hints:   = wceq 1364   dom cdm 4664

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 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-10 1519  ax-11 1520  ax-i12 1521  ax-bndl 1523  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-ext 2178

This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1475  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-nfc 2328  df-v 2765  df-un 3161  df-in 3163  df-ss 3170  df-sn 3629  df-pr 3630  df-op 3632  df-br 4035  df-dm 4674

This theorem is referenced by:  dmxpm  4887  dmxpid  4888  dmxpin  4889  rncoss  4937  rncoeq  4940  rnun  5079  rnin  5080  rnxpm  5100  rnxpss  5102  imainrect  5116  dmpropg  5143  dmtpop  5146  rnsnopg  5149  fntpg  5315  fnreseql  5675  dmoprab  6007  reldmmpo  6038  elmpocl  6122  tfrlem8  6385  tfr2a  6388  tfrlemi14d  6400  tfr1onlemres  6416  tfri1dALT  6418  tfrcllemres  6429  xpassen  6898  sbthlemi5  7036  casedm  7161  djudm  7180  ctssdccl  7186  dmaddpi  7409  dmmulpi  7410  dmaddpq  7463  dmmulpq  7464  axaddf  7952  axmulf  7953  ennnfonelemom  12650  ennnfonelemdm  12662