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Theorem f1fun 5607
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 5606 . 2  |-  ( F : A -1-1-> B  ->  F  Fn  A )
2 fnfun 5507 . 2  |-  ( F  Fn  A  ->  Fun  F )
31, 2syl 16 1  |-  ( F : A -1-1-> B  ->  Fun  F )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   Fun wfun 5411    Fn wfn 5412   -1-1->wf1 5414
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 371  df-fn 5420  df-f 5421  df-f1 5422
This theorem is referenced by:  f1cocnv2  5667  f1o2ndf1  6679  fnwelem  6686  fsuppco  7650  ackbij1b  8407  fin23lem31  8511  fin1a2lem6  8573  hashimarn  12199  gsumval3lem1  16382  gsumval3lem2  16383  usgrafun  23276  elhf  28211
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