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Theorem rneqi 4737
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
StepHypRef Expression
1 rneqi.1 . 2  |-  A  =  B
2 rneq 4736 . 2  |-  ( A  =  B  ->  ran  A  =  ran  B )
31, 2ax-mp 5 1  |-  ran  A  =  ran  B
Colors of variables: wff set class
Syntax hints:    = wceq 1316   ran crn 4510
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-3an 949  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-v 2662  df-un 3045  df-in 3047  df-ss 3054  df-sn 3503  df-pr 3504  df-op 3506  df-br 3900  df-opab 3960  df-cnv 4517  df-dm 4519  df-rn 4520
This theorem is referenced by:  rnmpt  4757  resima  4822  resima2  4823  ima0  4868  rnuni  4920  imaundi  4921  imaundir  4922  inimass  4925  dminxp  4953  imainrect  4954  xpima1  4955  xpima2m  4956  rnresv  4968  imacnvcnv  4973  rnpropg  4988  imadmres  5001  mptpreima  5002  dmco  5017  resdif  5357  fpr  5570  fprg  5571  fliftfuns  5667  rnoprab  5822  rnmpo  5849  qliftfuns  6481  xpassen  6692  sbthlemi6  6818  ennnfonelemrn  11859  cnconst2  12329
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