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Theorem f1fn 5166
Description: A one-to-one mapping is a function on its domain. (Contributed by NM, 8-Mar-2014.)
Assertion
Ref Expression
f1fn  |-  ( F : A -1-1-> B  ->  F  Fn  A )

Proof of Theorem f1fn
StepHypRef Expression
1 f1f 5164 . 2  |-  ( F : A -1-1-> B  ->  F : A --> B )
2 ffn 5114 . 2  |-  ( F : A --> B  ->  F  Fn  A )
31, 2syl 14 1  |-  ( F : A -1-1-> B  ->  F  Fn  A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    Fn wfn 4964   -->wf 4965   -1-1->wf1 4966
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104
This theorem depends on definitions:  df-bi 115  df-f 4973  df-f1 4974
This theorem is referenced by:  f1fun  5167  f1rel  5168  f1dm  5169  f1ssr  5171  f1f1orn  5212  f1elima  5492  f1eqcocnv  5510  f1oiso  5544  phplem4dom  6508  f1finf1o  6580  updjudhcoinlf  6678  updjudhcoinrg  6679  updjud  6680  fihashf1rn  10032
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