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Theorem fofn 5139
Description: An onto mapping is a function on its domain. (Contributed by NM, 16-Dec-2008.)
Assertion
Ref Expression
fofn  |-  ( F : A -onto-> B  ->  F  Fn  A )

Proof of Theorem fofn
StepHypRef Expression
1 fof 5137 . 2  |-  ( F : A -onto-> B  ->  F : A --> B )
2 ffn 5077 . 2  |-  ( F : A --> B  ->  F  Fn  A )
31, 2syl 14 1  |-  ( F : A -onto-> B  ->  F  Fn  A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    Fn wfn 4927   -->wf 4928   -onto->wfo 4930
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-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-in 2980  df-ss 2987  df-f 4936  df-fo 4938
This theorem is referenced by:  fodmrnu  5145  foun  5176  fo00  5193  cbvfo  5456  cbvexfo  5457  foeqcnvco  5461  1stcof  5821  2ndcof  5822  1stexg  5825  2ndexg  5826  df1st2  5871  df2nd2  5872  1stconst  5873  2ndconst  5874
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