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Theorem f1fun 5439
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 5438 . 2  |-  ( F : A -1-1-> B  ->  F  Fn  A )
2 fnfun 5341 . 2  |-  ( F  Fn  A  ->  Fun  F )
31, 2syl 15 1  |-  ( F : A -1-1-> B  ->  Fun  F )
Colors of variables: wff set class
Syntax hints:    -> wi 4   Fun wfun 5249    Fn wfn 5250   -1-1->wf1 5252
This theorem is referenced by:  f1cocnv2  5501  fnwelem  6230  ackbij1b  7865  fin23lem31  7969  fin1a2lem6  8031  elhf  24804  usgrafun  28108  usgraedgop  28109
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 177  df-an 360  df-fn 5258  df-f 5259  df-f1 5260
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