Theorem rneqi 4848

Description: Equality inference for range. (Contributed by NM, 4-Mar-2004.)

Hypothesis

Ref	Expression
rneqi.1	|- A = B

Assertion

Ref	Expression
rneqi	|- ran A = ran B

Proof of Theorem rneqi

Step	Hyp	Ref	Expression
1		rneqi.1	. 2 |- A = B
2		rneq 4847	. 2 |- ( A = B -> ran A = ran B )
3	1, 2	ax-mp 5	1 |- ran A = ran B

Syntax hints:   = wceq 1353   ran crn 4621

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 1445  ax-7 1446  ax-gen 1447  ax-ie1 1491  ax-ie2 1492  ax-8 1502  ax-10 1503  ax-11 1504  ax-i12 1505  ax-bndl 1507  ax-4 1508  ax-17 1524  ax-i9 1528  ax-ial 1532  ax-i5r 1533  ax-ext 2157

This theorem depends on definitions:  df-bi 117  df-3an 980  df-tru 1356  df-nf 1459  df-sb 1761  df-clab 2162  df-cleq 2168  df-clel 2171  df-nfc 2306  df-v 2737  df-un 3131  df-in 3133  df-ss 3140  df-sn 3595  df-pr 3596  df-op 3598  df-br 3999  df-opab 4060  df-cnv 4628  df-dm 4630  df-rn 4631

This theorem is referenced by:  rnmpt  4868  resima  4933  resima2  4934  ima0  4980  rnuni  5032  imaundi  5033  imaundir  5034  inimass  5037  dminxp  5065  imainrect  5066  xpima1  5067  xpima2m  5068  rnresv  5080  imacnvcnv  5085  rnpropg  5100  imadmres  5113  mptpreima  5114  dmco  5129  resdif  5475  fpr  5690  fprg  5691  fliftfuns  5789  rnoprab  5948  rnmpo  5975  qliftfuns  6609  xpassen  6820  sbthlemi6  6951  ennnfonelemrn  12385  cnconst2  13284