Theorem fofn 5128

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

Step	Hyp	Ref	Expression
1		fof 5126	. 2 |- ( F : A -onto-> B -> F : A --> B )
2		ffn 5066	. 2 |- ( F : A --> B -> F Fn A )
3	1, 2	syl 14	1 |- ( F : A -onto-> B -> F Fn A )

Syntax hints:   -> wi 4   Fn wfn 4917   -->wf 4918   -onto->wfo 4920

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 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-11 1437  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-in 2979  df-ss 2986  df-f 4926  df-fo 4928

This theorem is referenced by:  fodmrnu  5134  foun  5165  fo00  5182  cbvfo  5445  cbvexfo  5446  foeqcnvco  5450  1stcof  5810  2ndcof  5811  1stexg  5814  2ndexg  5815  df1st2  5860  df2nd2  5861  1stconst  5862  2ndconst  5863