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Theorem f1ofn 5158
Description: A one-to-one onto mapping is function on its domain. (Contributed by NM, 12-Dec-2003.)
Assertion
Ref Expression
f1ofn  |-  ( F : A -1-1-onto-> B  ->  F  Fn  A )

Proof of Theorem f1ofn
StepHypRef Expression
1 f1of 5157 . 2  |-  ( F : A -1-1-onto-> B  ->  F : A
--> B )
2 ffn 5077 . 2  |-  ( F : A --> B  ->  F  Fn  A )
31, 2syl 14 1  |-  ( F : A -1-1-onto-> B  ->  F  Fn  A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    Fn wfn 4927   -->wf 4928   -1-1-onto->wf1o 4931
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 4936  df-f1 4937  df-f1o 4939
This theorem is referenced by:  f1ofun  5159  f1odm  5161  isocnv2  5483  isoini  5488  isoselem  5490  bren  6294  en1  6346  xpen  6386  phplem4  6390  phplem4on  6402  dif1en  6414  supisolem  6480  ordiso2  6505
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