Theorem dmeqi 4879

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 4878	. 2 |- ( A = B -> dom A = dom B )
3	1, 2	ax-mp 5	1 |- dom A = dom B

Syntax hints:   = wceq 1373   dom cdm 4675

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 4045  df-dm 4685

This theorem is referenced by:  dmxpm  4898  dmxpid  4899  dmxpin  4900  rncoss  4949  rncoeq  4952  rnun  5091  rnin  5092  rnxpm  5112  rnxpss  5114  imainrect  5128  dmpropg  5155  dmtpop  5158  rnsnopg  5161  fntpg  5330  fnreseql  5690  dmoprab  6026  reldmmpo  6057  elmpocl  6141  tfrlem8  6404  tfr2a  6407  tfrlemi14d  6419  tfr1onlemres  6435  tfri1dALT  6437  tfrcllemres  6448  xpassen  6925  sbthlemi5  7063  casedm  7188  djudm  7207  ctssdccl  7213  dmaddpi  7438  dmmulpi  7439  dmaddpq  7492  dmmulpq  7493  axaddf  7981  axmulf  7982  ennnfonelemom  12779  ennnfonelemdm  12791  structiedg0val  15637