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Theorem rnresi 6093
Description: The range of the restricted identity function. (Contributed by NM, 27-Aug-2004.)
Assertion
Ref Expression
rnresi ran ( I ↾ 𝐴) = 𝐴

Proof of Theorem rnresi
StepHypRef Expression
1 df-ima 5698 . 2 ( I “ 𝐴) = ran ( I ↾ 𝐴)
2 imai 6092 . 2 ( I “ 𝐴) = 𝐴
31, 2eqtr3i 2767 1 ran ( I ↾ 𝐴) = 𝐴
Colors of variables: wff setvar class
Syntax hints:   = wceq 1540   I cid 5577  ran crn 5686  cres 5687  cima 5688
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708  ax-sep 5296  ax-nul 5306  ax-pr 5432
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-ral 3062  df-rex 3071  df-rab 3437  df-v 3482  df-dif 3954  df-un 3956  df-in 3958  df-ss 3968  df-nul 4334  df-if 4526  df-sn 4627  df-pr 4629  df-op 4633  df-br 5144  df-opab 5206  df-id 5578  df-xp 5691  df-rel 5692  df-cnv 5693  df-dm 5695  df-rn 5696  df-res 5697  df-ima 5698
This theorem is referenced by:  resiima  6094  iordsmo  8397  dfac9  10177  relexprng  15085  relexpfld  15088  restid2  17475  sylow1lem2  19617  sylow3lem1  19645  lsslinds  21851  wilthlem3  27113  ausgrusgrb  29182  umgrres1lem  29327  umgrres1  29331  nbupgrres  29381  cusgrexilem2  29459  cusgrsize  29472  cycpmconjslem2  33175  diophrw  42770  lnrfg  43131  rclexi  43628  cnvrcl0  43638  dfrtrcl5  43642  dfrcl2  43687  brfvrcld2  43705  iunrelexp0  43715  relexpiidm  43717  relexp01min  43726  dvsid  44350  fourierdlem60  46181  fourierdlem61  46182  stgredg  47923  gpgedg  48004  uspgrsprfo  48064
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