Theorem fofn 5479

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 5477	. 2 |- ( F : A -onto-> B -> F : A --> B )
2		ffn 5404	. 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 5250   -->wf 5251   -onto->wfo 5253

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 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-11 1517  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-in 3160  df-ss 3167  df-f 5259  df-fo 5261

This theorem is referenced by:  fodmrnu  5485  foun  5520  fo00  5537  foelcdmi  5610  foima2  5795  cbvfo  5829  cbvexfo  5830  foeqcnvco  5834  canth  5872  1stcof  6218  2ndcof  6219  1stexg  6222  2ndexg  6223  df1st2  6274  df2nd2  6275  1stconst  6276  2ndconst  6277  fidcenumlemrks  7014  fidcenumlemr  7016  ctm  7170  suplocexprlemell  7775  ennnfonelemhf1o  12573  ennnfonelemrn  12579  imasaddfnlemg  12900  imasgrp2  13183  imasrng  13455  imasring  13563  znf1o  14150  upxp  14451  uptx  14453  cnmpt1st  14467  cnmpt2nd  14468  pw1nct  15563