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Theorem rnresi 6094
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 5701 . 2 ( I “ 𝐴) = ran ( I ↾ 𝐴)
2 imai 6093 . 2 ( I “ 𝐴) = 𝐴
31, 2eqtr3i 2764 1 ran ( I ↾ 𝐴) = 𝐴
Colors of variables: wff setvar class
Syntax hints:   = wceq 1536   I cid 5581  ran crn 5689  cres 5690  cima 5691
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1791  ax-4 1805  ax-5 1907  ax-6 1964  ax-7 2004  ax-8 2107  ax-9 2115  ax-ext 2705  ax-sep 5301  ax-nul 5311  ax-pr 5437
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1539  df-fal 1549  df-ex 1776  df-sb 2062  df-clab 2712  df-cleq 2726  df-clel 2813  df-ral 3059  df-rex 3068  df-rab 3433  df-v 3479  df-dif 3965  df-un 3967  df-in 3969  df-ss 3979  df-nul 4339  df-if 4531  df-sn 4631  df-pr 4633  df-op 4637  df-br 5148  df-opab 5210  df-id 5582  df-xp 5694  df-rel 5695  df-cnv 5696  df-dm 5698  df-rn 5699  df-res 5700  df-ima 5701
This theorem is referenced by:  resiima  6095  iordsmo  8395  dfac9  10174  relexprng  15081  relexpfld  15084  restid2  17476  sylow1lem2  19631  sylow3lem1  19659  lsslinds  21868  wilthlem3  27127  ausgrusgrb  29196  umgrres1lem  29341  umgrres1  29345  nbupgrres  29395  cusgrexilem2  29473  cusgrsize  29486  cycpmconjslem2  33157  diophrw  42746  lnrfg  43107  rclexi  43604  cnvrcl0  43614  dfrtrcl5  43618  dfrcl2  43663  brfvrcld2  43681  iunrelexp0  43691  relexpiidm  43693  relexp01min  43702  dvsid  44326  fourierdlem60  46121  fourierdlem61  46122  stgredg  47858  gpgedg  47939  uspgrsprfo  47991
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