Theorem fofn 5271

Description: An onto mapping is a function on its domain. (Contributed by set.mm contributors, 16-Dec-2008.)

Assertion

Ref	Expression
fofn	⊢ (F:A–onto→B → F Fn A)

Proof of Theorem fofn

Step	Hyp	Ref	Expression
1		fof 5269	. 2 ⊢ (F:A–onto→B → F:A–→B)
2		ffn 5223	. 2 ⊢ (F:A–→B → F Fn A)
3	1, 2	syl 15	1 ⊢ (F:A–onto→B → F Fn A)

Syntax hints:   → wi 4   Fn wfn 4776  –→wf 4777  –onto→wfo 4779

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259  df-f 4791  df-fo 4793

This theorem is referenced by:  fodmrnu  5277  fo00  5318  opfv1st  5514  opfv2nd  5515  fundmen  6043  xpassen  6057