Theorem fofn 5502

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 5500	. 2 |- ( F : A -onto-> B -> F : A --> B )
2		ffn 5427	. 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 5267   -->wf 5268   -onto->wfo 5270

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 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-11 1529  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-in 3172  df-ss 3179  df-f 5276  df-fo 5278

This theorem is referenced by:  fodmrnu  5508  foun  5543  fo00  5560  foelcdmi  5633  foima2  5822  cbvfo  5856  cbvexfo  5857  foeqcnvco  5861  canth  5899  1stcof  6251  2ndcof  6252  1stexg  6255  2ndexg  6256  df1st2  6307  df2nd2  6308  1stconst  6309  2ndconst  6310  fidcenumlemrks  7057  fidcenumlemr  7059  ctm  7213  suplocexprlemell  7828  ennnfonelemhf1o  12817  ennnfonelemrn  12823  imasaddfnlemg  13179  imasmnd2  13317  imasgrp2  13479  imasrng  13751  imasring  13859  znf1o  14446  upxp  14777  uptx  14779  cnmpt1st  14793  cnmpt2nd  14794  pw1nct  15977