Theorem fofn 5592

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 5590	. 2 |- ( F : A -onto-> B -> F : A --> B )
2		ffn 5508	. 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 5347   -->wf 5348   -onto->wfo 5350

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 2214

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-sb 1812  df-clab 2219  df-cleq 2225  df-clel 2228  df-in 3217  df-ss 3224  df-f 5356  df-fo 5358

This theorem is referenced by:  fodmrnu  5598  foun  5633  fo00  5652  foelcdmi  5729  foima2  5924  cbvfo  5958  cbvexfo  5959  foeqcnvco  5963  canth  6001  1stcof  6357  2ndcof  6358  1stexg  6361  2ndexg  6362  df1st2  6415  df2nd2  6416  1stconst  6417  2ndconst  6418  fidcenumlemrks  7223  fidcenumlemr  7225  ctm  7400  suplocexprlemell  8028  ennnfonelemhf1o  13164  ennnfonelemrn  13170  imasaddfnlemg  13527  imasmnd2  13665  imasgrp2  13827  imasrng  14100  imasring  14208  znf1o  14799  upxp  15137  uptx  15139  cnmpt1st  15153  cnmpt2nd  15154  pw1nct  16777