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Theorem fofn 5033
Description: An onto mapping is a function on its domain. (Contributed by NM, 16-Dec-2008.)
Assertion
Ref Expression
fofn (𝐹:AontoB𝐹 Fn A)

Proof of Theorem fofn
StepHypRef Expression
1 fof 5031 . 2 (𝐹:AontoB𝐹:AB)
2 ffn 4972 . 2 (𝐹:AB𝐹 Fn A)
31, 2syl 14 1 (𝐹:AontoB𝐹 Fn A)
Colors of variables: wff set class
Syntax hints:  wi 4   Fn wfn 4824  wf 4825  ontowfo 4827
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-11 1378  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-in 2901  df-ss 2908  df-f 4833  df-fo 4835
This theorem is referenced by:  fodmrnu  5039  foun  5070  fo00  5087  cbvfo  5350  cbvexfo  5351  foeqcnvco  5355  1stcof  5713  2ndcof  5714  1stexg  5717  2ndexg  5718  df1st2  5763  df2nd2  5764  1stconst  5765  2ndconst  5766
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