ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  rnresi Unicode version

Theorem rnresi 4852
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 4510 . 2  |-  (  _I  " A )  =  ran  (  _I  |`  A )
2 imai 4851 . 2  |-  (  _I  " A )  =  A
31, 2eqtr3i 2135 1  |-  ran  (  _I  |`  A )  =  A
Colors of variables: wff set class
Syntax hints:    = wceq 1312    _I cid 4168   ran crn 4498    |` cres 4499   "cima 4500
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1404  ax-7 1405  ax-gen 1406  ax-ie1 1450  ax-ie2 1451  ax-8 1463  ax-10 1464  ax-11 1465  ax-i12 1466  ax-bndl 1467  ax-4 1468  ax-14 1473  ax-17 1487  ax-i9 1491  ax-ial 1495  ax-i5r 1496  ax-ext 2095  ax-sep 4004  ax-pow 4056  ax-pr 4089
This theorem depends on definitions:  df-bi 116  df-3an 945  df-tru 1315  df-nf 1418  df-sb 1717  df-eu 1976  df-mo 1977  df-clab 2100  df-cleq 2106  df-clel 2109  df-nfc 2242  df-ral 2393  df-rex 2394  df-v 2657  df-un 3039  df-in 3041  df-ss 3048  df-pw 3476  df-sn 3497  df-pr 3498  df-op 3500  df-br 3894  df-opab 3948  df-id 4173  df-xp 4503  df-rel 4504  df-cnv 4505  df-dm 4507  df-rn 4508  df-res 4509  df-ima 4510
This theorem is referenced by:  resiima  4853  iordsmo  6146  restid2  11966
  Copyright terms: Public domain W3C validator