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Theorem f1fun 5443
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 5442 . 2  |-  ( F : A -1-1-> B  ->  F  Fn  A )
2 fnfun 5332 . 2  |-  ( F  Fn  A  ->  Fun  F )
31, 2syl 14 1  |-  ( F : A -1-1-> B  ->  Fun  F )
Colors of variables: wff set class
Syntax hints:    -> wi 4   Fun wfun 5229    Fn wfn 5230   -1-1->wf1 5232
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106
This theorem depends on definitions:  df-bi 117  df-fn 5238  df-f 5239  df-f1 5240
This theorem is referenced by:  f1cocnv2  5508  f1o2ndf1  6252  f1dmvrnfibi  6972  djuinj  7134
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