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Theorem dfrn4 6152
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 5644 . 2 (𝐴 “ V) = ran (𝐴 ↾ V)
2 rnresv 6151 . 2 ran (𝐴 ↾ V) = ran 𝐴
31, 2eqtr2i 2765 1 ran 𝐴 = (𝐴 “ V)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1541  Vcvv 3443  ran crn 5632  cres 5633  cima 5634
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2707  ax-sep 5254  ax-nul 5261  ax-pr 5382
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-3an 1089  df-tru 1544  df-fal 1554  df-ex 1782  df-sb 2068  df-clab 2714  df-cleq 2728  df-clel 2814  df-rab 3406  df-v 3445  df-dif 3911  df-un 3913  df-in 3915  df-ss 3925  df-nul 4281  df-if 4485  df-sn 4585  df-pr 4587  df-op 4591  df-br 5104  df-opab 5166  df-xp 5637  df-rel 5638  df-cnv 5639  df-dm 5641  df-rn 5642  df-res 5643  df-ima 5644
This theorem is referenced by:  csbrn  6153  dmmpt  6190  gsumpropd2lem  18488  ffsrn  31488
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