Theorem fofn 5500

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 5498	. 2 |- ( F : A -onto-> B -> F : A --> B )
2		ffn 5425	. 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 5266   -->wf 5267   -onto->wfo 5269

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 5275  df-fo 5277

This theorem is referenced by:  fodmrnu  5506  foun  5541  fo00  5558  foelcdmi  5631  foima2  5820  cbvfo  5854  cbvexfo  5855  foeqcnvco  5859  canth  5897  1stcof  6249  2ndcof  6250  1stexg  6253  2ndexg  6254  df1st2  6305  df2nd2  6306  1stconst  6307  2ndconst  6308  fidcenumlemrks  7055  fidcenumlemr  7057  ctm  7211  suplocexprlemell  7826  ennnfonelemhf1o  12784  ennnfonelemrn  12790  imasaddfnlemg  13146  imasmnd2  13284  imasgrp2  13446  imasrng  13718  imasring  13826  znf1o  14413  upxp  14744  uptx  14746  cnmpt1st  14760  cnmpt2nd  14761  pw1nct  15940