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Theorem f1ofo 5164
Description: A one-to-one onto function is an onto function. (Contributed by NM, 28-Apr-2004.)
Assertion
Ref Expression
f1ofo  |-  ( F : A -1-1-onto-> B  ->  F : A -onto-> B )

Proof of Theorem f1ofo
StepHypRef Expression
1 dff1o3 5163 . 2  |-  ( F : A -1-1-onto-> B  <->  ( F : A -onto-> B  /\  Fun  `' F ) )
21simplbi 268 1  |-  ( F : A -1-1-onto-> B  ->  F : A -onto-> B )
Colors of variables: wff set class
Syntax hints:    -> wi 4   `'ccnv 4370   Fun wfun 4926   -onto->wfo 4930   -1-1-onto->wf1o 4931
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-3an 922  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-in 2980  df-ss 2987  df-f 4936  df-f1 4937  df-fo 4938  df-f1o 4939
This theorem is referenced by:  f1imacnv  5174  f1ococnv2  5184  fo00  5193  isoini  5488  isoselem  5490  f1opw2  5737  f1dmex  5774  bren  6294  f1oeng  6304  en1  6346  phplem4  6390  phplem4on  6402  dif1en  6414  supisolem  6480  ordiso2  6505  1fv  9226
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