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Theorem dfrn4 5272
Description: Range defined in terms of image. (Contributed by NM, 14-May-2008.)
Assertion
Ref Expression
dfrn4  |-  ran  A  =  ( A " _V )

Proof of Theorem dfrn4
StepHypRef Expression
1 df-ima 4832 . 2  |-  ( A
" _V )  =  ran  ( A  |`  _V )
2 rnresv 5271 . 2  |-  ran  ( A  |`  _V )  =  ran  A
31, 2eqtr2i 2409 1  |-  ran  A  =  ( A " _V )
Colors of variables: wff set class
Syntax hints:    = wceq 1649   _Vcvv 2900   ran crn 4820    |` cres 4821   "cima 4822
This theorem is referenced by:  dmmpt  5306  gsumpropd2lem  24050
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-14 1721  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2369  ax-sep 4272  ax-nul 4280  ax-pr 4345
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2243  df-mo 2244  df-clab 2375  df-cleq 2381  df-clel 2384  df-nfc 2513  df-ne 2553  df-ral 2655  df-rex 2656  df-rab 2659  df-v 2902  df-dif 3267  df-un 3269  df-in 3271  df-ss 3278  df-nul 3573  df-if 3684  df-sn 3764  df-pr 3765  df-op 3767  df-br 4155  df-opab 4209  df-xp 4825  df-rel 4826  df-cnv 4827  df-dm 4829  df-rn 4830  df-res 4831  df-ima 4832
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