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

Theorem rnresv 5100
Description: The range of a universal restriction. (Contributed by NM, 14-May-2008.)
Assertion
Ref Expression
rnresv  |-  ran  ( A  |`  _V )  =  ran  A

Proof of Theorem rnresv
StepHypRef Expression
1 cnvcnv2 5094 . . 3  |-  `' `' A  =  ( A  |` 
_V )
21rneqi 4867 . 2  |-  ran  `' `' A  =  ran  ( A  |`  _V )
3 rncnvcnv 4864 . 2  |-  ran  `' `' A  =  ran  A
42, 3eqtr3i 2210 1  |-  ran  ( A  |`  _V )  =  ran  A
Colors of variables: wff set class
Syntax hints:    = wceq 1363   _Vcvv 2749   `'ccnv 4637   ran crn 4639    |` cres 4640
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-14 2161  ax-ext 2169  ax-sep 4133  ax-pow 4186  ax-pr 4221
This theorem depends on definitions:  df-bi 117  df-3an 981  df-tru 1366  df-nf 1471  df-sb 1773  df-eu 2039  df-mo 2040  df-clab 2174  df-cleq 2180  df-clel 2183  df-nfc 2318  df-ral 2470  df-rex 2471  df-v 2751  df-un 3145  df-in 3147  df-ss 3154  df-pw 3589  df-sn 3610  df-pr 3611  df-op 3613  df-br 4016  df-opab 4077  df-xp 4644  df-rel 4645  df-cnv 4646  df-dm 4648  df-rn 4649  df-res 4650
This theorem is referenced by:  dfrn4  5101  casefun  7098
  Copyright terms: Public domain W3C validator