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Theorem dfrn4 6200
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 5685 . 2 (𝐴 “ V) = ran (𝐴 ↾ V)
2 rnresv 6199 . 2 ran (𝐴 ↾ V) = ran 𝐴
31, 2eqtr2i 2757 1 ran 𝐴 = (𝐴 “ V)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1534  Vcvv 3470  ran crn 5673  cres 5674  cima 5675
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2699  ax-sep 5293  ax-nul 5300  ax-pr 5423
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 847  df-3an 1087  df-tru 1537  df-fal 1547  df-ex 1775  df-sb 2061  df-clab 2706  df-cleq 2720  df-clel 2806  df-rab 3429  df-v 3472  df-dif 3948  df-un 3950  df-in 3952  df-ss 3962  df-nul 4319  df-if 4525  df-sn 4625  df-pr 4627  df-op 4631  df-br 5143  df-opab 5205  df-xp 5678  df-rel 5679  df-cnv 5680  df-dm 5682  df-rn 5683  df-res 5684  df-ima 5685
This theorem is referenced by:  csbrn  6201  dmmpt  6238  gsumpropd2lem  18632  ffsrn  32505
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