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Theorem rnresi 5044
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 4718 . 2  |-  (  _I  " A )  =  ran  (  _I  |`  A )
2 imai 5043 . 2  |-  (  _I  " A )  =  A
31, 2eqtr3i 2318 1  |-  ran  (  _I  |`  A )  =  A
Colors of variables: wff set class
Syntax hints:    = wceq 1632    _I cid 4320   ran crn 4706    |` cres 4707   "cima 4708
This theorem is referenced by:  resiima  5045  iordsmo  6390  dfac9  7778  restid2  13351  sylow1lem2  14926  sylow3lem1  14954  wilthlem3  20324  relexprn  24048  dispos  25390  diophrw  26941  lsslinds  27404  lnrfg  27426  dvsid  27651
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-nul 4165  ax-pr 4230
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-mo 2161  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rex 2562  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-br 4040  df-opab 4094  df-id 4325  df-xp 4711  df-rel 4712  df-cnv 4713  df-dm 4715  df-rn 4716  df-res 4717  df-ima 4718
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