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Theorem f1fun 5766
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 5765 . 2  |-  ( F : A -1-1-> B  ->  F  Fn  A )
2 fnfun 5659 . 2  |-  ( F  Fn  A  ->  Fun  F )
31, 2syl 17 1  |-  ( F : A -1-1-> B  ->  Fun  F )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   Fun wfun 5563    Fn wfn 5564   -1-1->wf1 5566
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 369  df-fn 5572  df-f 5573  df-f1 5574
This theorem is referenced by:  f1cocnv2  5826  f1o2ndf1  6892  fnwelem  6899  fsuppco  7895  ackbij1b  8651  fin23lem31  8755  fin1a2lem6  8817  hashimarn  12545  gsumval3lem1  17233  gsumval3lem2  17234  usgrafun  24766  elhf  30512  f1dmvrnfibi  37945
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