Theorem fofn 5597

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 5595	. 2 |- ( F : A -onto-> B -> F : A --> B )
2		ffn 5513	. 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 5352   -->wf 5353   -onto->wfo 5355

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 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-11 1555  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2216

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-sb 1812  df-clab 2221  df-cleq 2227  df-clel 2230  df-in 3220  df-ss 3227  df-f 5361  df-fo 5363

This theorem is referenced by:  fodmrnu  5603  foun  5638  fo00  5657  foelcdmi  5734  foima2  5930  cbvfo  5964  cbvexfo  5965  foeqcnvco  5969  canth  6009  1stcof  6370  2ndcof  6371  1stexg  6374  2ndexg  6375  df1st2  6428  df2nd2  6429  1stconst  6430  2ndconst  6431  fidcenumlemrks  7236  fidcenumlemr  7238  ctm  7413  suplocexprlemell  8044  ennnfonelemhf1o  13248  ennnfonelemrn  13254  imasaddfnlemg  13578  imasmnd2  13707  imasgrp2  13863  imasrng  14195  imasring  14307  znf1o  14925  upxp  15263  uptx  15265  cnmpt1st  15279  cnmpt2nd  15280  pw1nct  16903