Theorem fofn 5482

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 5480	. 2 |- ( F : A -onto-> B -> F : A --> B )
2		ffn 5407	. 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 5253   -->wf 5254   -onto->wfo 5256

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 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-11 1520  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-ext 2178

This theorem depends on definitions:  df-bi 117  df-nf 1475  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-in 3163  df-ss 3170  df-f 5262  df-fo 5264

This theorem is referenced by:  fodmrnu  5488  foun  5523  fo00  5540  foelcdmi  5613  foima2  5798  cbvfo  5832  cbvexfo  5833  foeqcnvco  5837  canth  5875  1stcof  6221  2ndcof  6222  1stexg  6225  2ndexg  6226  df1st2  6277  df2nd2  6278  1stconst  6279  2ndconst  6280  fidcenumlemrks  7019  fidcenumlemr  7021  ctm  7175  suplocexprlemell  7780  ennnfonelemhf1o  12630  ennnfonelemrn  12636  imasaddfnlemg  12957  imasgrp2  13240  imasrng  13512  imasring  13620  znf1o  14207  upxp  14508  uptx  14510  cnmpt1st  14524  cnmpt2nd  14525  pw1nct  15647