Theorem rneqi 4855

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 4854	. 2 |- ( A = B -> ran A = ran B )
3	1, 2	ax-mp 5	1 |- ran A = ran B

Syntax hints:   = wceq 1353   ran crn 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 2739  df-un 3133  df-in 3135  df-ss 3142  df-sn 3598  df-pr 3599  df-op 3601  df-br 4004  df-opab 4065  df-cnv 4634  df-dm 4636  df-rn 4637

This theorem is referenced by:  rnmpt  4875  resima  4940  resima2  4941  ima0  4987  rnuni  5040  imaundi  5041  imaundir  5042  inimass  5045  dminxp  5073  imainrect  5074  xpima1  5075  xpima2m  5076  rnresv  5088  imacnvcnv  5093  rnpropg  5108  imadmres  5121  mptpreima  5122  dmco  5137  resdif  5483  fpr  5698  fprg  5699  fliftfuns  5798  rnoprab  5957  rnmpo  5984  qliftfuns  6618  xpassen  6829  sbthlemi6  6960  ennnfonelemrn  12419  cnconst2  13703