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Theorem f1fun 5633
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 5632 . 2  |-  ( F : A -1-1-> B  ->  F  Fn  A )
2 fnfun 5534 . 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 5440    Fn wfn 5441   -1-1->wf1 5443
This theorem is referenced by:  f1cocnv2  5695  f1o2ndf1  6446  fnwelem  6453  ackbij1b  8111  fin23lem31  8215  fin1a2lem6  8277  usgrafun  21370  elhf  26107  hashimarn  28141
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 5449  df-f 5450  df-f1 5451
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