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Theorem rnresi 5219
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 4891 . 2  |-  (  _I  " A )  =  ran  (  _I  |`  A )
2 imai 5218 . 2  |-  (  _I  " A )  =  A
31, 2eqtr3i 2458 1  |-  ran  (  _I  |`  A )  =  A
Colors of variables: wff set class
Syntax hints:    = wceq 1652    _I cid 4493   ran crn 4879    |` cres 4880   "cima 4881
This theorem is referenced by:  resiima  5220  iordsmo  6619  dfac9  8016  restid2  13658  sylow1lem2  15233  sylow3lem1  15261  wilthlem3  20853  ausisusgra  21380  cusgraexi  21477  relexprn  25136  diophrw  26817  lsslinds  27278  lnrfg  27300  dvsid  27525
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-br 4213  df-opab 4267  df-id 4498  df-xp 4884  df-rel 4885  df-cnv 4886  df-dm 4888  df-rn 4889  df-res 4890  df-ima 4891
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