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Theorem f1fun 5462
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 5461 . 2  |-  ( F : A -1-1-> B  ->  F  Fn  A )
2 fnfun 5351 . 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 5248    Fn wfn 5249   -1-1->wf1 5251
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 5257  df-f 5258  df-f1 5259
This theorem is referenced by:  f1cocnv2  5528  f1o2ndf1  6281  f1dmvrnfibi  7003  djuinj  7165
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