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Theorem f1fun 5776
Description: A one-to-one mapping is a function. (Contributed by NM, 8-Mar-2014.)
Assertion
Ref Expression
f1fun  |-  ( F : A -1-1-> B  ->  Fun  F )

Proof of Theorem f1fun
StepHypRef Expression
1 f1fn 5775 . 2  |-  ( F : A -1-1-> B  ->  F  Fn  A )
2 fnfun 5671 . 2  |-  ( F  Fn  A  ->  Fun  F )
31, 2syl 16 1  |-  ( F : A -1-1-> B  ->  Fun  F )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   Fun wfun 5575    Fn wfn 5576   -1-1->wf1 5578
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 371  df-fn 5584  df-f 5585  df-f1 5586
This theorem is referenced by:  f1cocnv2  5836  f1o2ndf1  6883  fnwelem  6890  fsuppco  7852  ackbij1b  8610  fin23lem31  8714  fin1a2lem6  8776  hashimarn  12451  gsumval3lem1  16695  gsumval3lem2  16696  usgrafun  24014  elhf  29396  f1dmvrnfibi  31738
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