Theorem rneqi 4876

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 4875	. 2 |- ( A = B -> ran A = ran B )
3	1, 2	ax-mp 5	1 |- ran A = ran B

Syntax hints:   = wceq 1364   ran crn 4648

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 2171

This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-v 2754  df-un 3148  df-in 3150  df-ss 3157  df-sn 3616  df-pr 3617  df-op 3619  df-br 4022  df-opab 4083  df-cnv 4655  df-dm 4657  df-rn 4658

This theorem is referenced by:  rnmpt  4896  resima  4961  resima2  4962  ima0  5008  rnuni  5061  imaundi  5062  imaundir  5063  inimass  5066  dminxp  5094  imainrect  5095  xpima1  5096  xpima2m  5097  rnresv  5109  imacnvcnv  5114  rnpropg  5129  imadmres  5142  mptpreima  5143  dmco  5158  resdif  5505  fpr  5722  fprg  5723  fliftfuns  5823  rnoprab  5983  rnmpo  6011  qliftfuns  6649  xpassen  6860  sbthlemi6  6995  ennnfonelemrn  12481  cnconst2  14218