Theorem fofn 5440

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 5438	. 2 |- ( F : A -onto-> B -> F : A --> B )
2		ffn 5365	. 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 5211   -->wf 5212   -onto->wfo 5214

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-11 1506  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-in 3135  df-ss 3142  df-f 5220  df-fo 5222

This theorem is referenced by:  fodmrnu  5446  foun  5480  fo00  5497  foelcdmi  5568  foima2  5752  cbvfo  5785  cbvexfo  5786  foeqcnvco  5790  canth  5828  1stcof  6163  2ndcof  6164  1stexg  6167  2ndexg  6168  df1st2  6219  df2nd2  6220  1stconst  6221  2ndconst  6222  fidcenumlemrks  6951  fidcenumlemr  6953  ctm  7107  suplocexprlemell  7711  ennnfonelemhf1o  12413  ennnfonelemrn  12419  imasaddfnlemg  12734  upxp  13742  uptx  13744  cnmpt1st  13758  cnmpt2nd  13759  pw1nct  14722