Theorem fofn 5550

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 5548	. 2 |- ( F : A -onto-> B -> F : A --> B )
2		ffn 5473	. 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 5313   -->wf 5314   -onto->wfo 5316

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 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-11 1552  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-in 3203  df-ss 3210  df-f 5322  df-fo 5324

This theorem is referenced by:  fodmrnu  5556  foun  5591  fo00  5609  foelcdmi  5686  foima2  5875  cbvfo  5909  cbvexfo  5910  foeqcnvco  5914  canth  5952  1stcof  6309  2ndcof  6310  1stexg  6313  2ndexg  6314  df1st2  6365  df2nd2  6366  1stconst  6367  2ndconst  6368  fidcenumlemrks  7120  fidcenumlemr  7122  ctm  7276  suplocexprlemell  7900  ennnfonelemhf1o  12984  ennnfonelemrn  12990  imasaddfnlemg  13347  imasmnd2  13485  imasgrp2  13647  imasrng  13919  imasring  14027  znf1o  14615  upxp  14946  uptx  14948  cnmpt1st  14962  cnmpt2nd  14963  pw1nct  16369