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Theorem f1fun 5574
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 5573 . 2  |-  ( F : A -1-1-> B  ->  F  Fn  A )
2 fnfun 5475 . 2  |-  ( F  Fn  A  ->  Fun  F )
31, 2syl 16 1  |-  ( F : A -1-1-> B  ->  Fun  F )
Colors of variables: wff set class
Syntax hints:    -> wi 4   Fun wfun 5381    Fn wfn 5382   -1-1->wf1 5384
This theorem is referenced by:  f1cocnv2  5636  fnwelem  6390  ackbij1b  8045  fin23lem31  8149  fin1a2lem6  8211  hashf1rn  11556  usgrafun  21238  elhf  25822
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 178  df-an 361  df-fn 5390  df-f 5391  df-f1 5392
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