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Theorem ffrn 5968
 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 5958 . 2 (𝐹:𝐴𝐵𝐹 Fn 𝐴)
2 dffn3 5967 . 2 (𝐹 Fn 𝐴𝐹:𝐴⟶ran 𝐹)
31, 2sylib 207 1 (𝐹:𝐴𝐵𝐹:𝐴⟶ran 𝐹)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ran crn 5039   Fn wfn 5799  ⟶wf 5800 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-in 3547  df-ss 3554  df-f 5808 This theorem is referenced by:  volicoff  38888  frgrncvvdeqlemB  41477
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