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Theorem ffrn 6519
Description: A function maps to its range. (Contributed by Glauco Siliprandi, 3-Mar-2021.)
Assertion
Ref Expression
ffrn (𝐹:𝐴𝐵𝐹:𝐴⟶ran 𝐹)

Proof of Theorem ffrn
StepHypRef Expression
1 ffn 6507 . 2 (𝐹:𝐴𝐵𝐹 Fn 𝐴)
2 dffn3 6518 . 2 (𝐹 Fn 𝐴𝐹:𝐴⟶ran 𝐹)
31, 2sylib 219 1 (𝐹:𝐴𝐵𝐹:𝐴⟶ran 𝐹)
Colors of variables: wff setvar class
Syntax hints:  wi 4  ran crn 5549   Fn wfn 6343  wf 6344
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2151  ax-12 2167  ax-ext 2790
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-tru 1531  df-ex 1772  df-nf 1776  df-sb 2061  df-clab 2797  df-cleq 2811  df-clel 2890  df-in 3940  df-ss 3949  df-f 6352
This theorem is referenced by:  fo2ndf  7806  mapsnd  8438  itg1val2  24212  selvval2lem4  39014  volicoff  42157  fundcmpsurbijinjpreimafv  43444
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