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Theorem ffrn 6750
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 6737 . 2 (𝐹:𝐴𝐵𝐹 Fn 𝐴)
2 dffn3 6749 . 2 (𝐹 Fn 𝐴𝐹:𝐴⟶ran 𝐹)
31, 2sylib 218 1 (𝐹:𝐴𝐵𝐹:𝐴⟶ran 𝐹)
Colors of variables: wff setvar class
Syntax hints:  wi 4  ran crn 5690   Fn wfn 6558  wf 6559
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792
This theorem depends on definitions:  df-bi 207  df-an 396  df-ss 3980  df-f 6567
This theorem is referenced by:  fo2ndf  8145  mapsnd  8925  itg1val2  25733  aks6d1c6lem3  42154  volicoff  45951  f1cof1b  47027  f1ocof1ob  47031  fundcmpsurbijinjpreimafv  47332
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