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Theorem fofn 5235
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 5233 . 2  |-  ( F : A -onto-> B  ->  F : A --> B )
2 ffn 5161 . 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 5010   -->wf 5011   -onto->wfo 5013
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 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-11 1442  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-in 3005  df-ss 3012  df-f 5019  df-fo 5021
This theorem is referenced by:  fodmrnu  5241  foun  5272  fo00  5289  foima2  5530  cbvfo  5564  cbvexfo  5565  foeqcnvco  5569  1stcof  5934  2ndcof  5935  1stexg  5938  2ndexg  5939  df1st2  5984  df2nd2  5985  1stconst  5986  2ndconst  5987  fidcenumlemrks  6662  fidcenumlemr  6664
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