Theorem rneqi 4891

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 4890	. 2 |- ( A = B -> ran A = ran B )
3	1, 2	ax-mp 5	1 |- ran A = ran B

Syntax hints:   = wceq 1364   ran crn 4661

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 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-v 2762  df-un 3158  df-in 3160  df-ss 3167  df-sn 3625  df-pr 3626  df-op 3628  df-br 4031  df-opab 4092  df-cnv 4668  df-dm 4670  df-rn 4671

This theorem is referenced by:  rnmpt  4911  resima  4976  resima2  4977  mptima  5018  ima0  5025  rnuni  5078  imaundi  5079  imaundir  5080  inimass  5083  dminxp  5111  imainrect  5112  xpima1  5113  xpima2m  5114  rnresv  5126  imacnvcnv  5131  rnpropg  5146  imadmres  5159  mptpreima  5160  dmco  5175  resdif  5523  fpr  5741  fprg  5742  fliftfuns  5842  rnoprab  6002  rnmpo  6030  qliftfuns  6675  xpassen  6886  sbthlemi6  7023  ennnfonelemrn  12579  cnconst2  14412  elply2  14914