Theorem f1ofn 5288

Description: A one-to-one onto mapping is function on its domain. (Contributed by set.mm contributors, 12-Dec-2003.)

Assertion

Ref	Expression
f1ofn	⊢ (F:A–1-1-onto→B → F Fn A)

Proof of Theorem f1ofn

Step	Hyp	Ref	Expression
1		f1of 5287	. 2 ⊢ (F:A–1-1-onto→B → F:A–→B)
2		ffn 5223	. 2 ⊢ (F:A–→B → F Fn A)
3	1, 2	syl 15	1 ⊢ (F:A–1-1-onto→B → F Fn A)

Syntax hints:   → wi 4   Fn wfn 4776  –→wf 4777  –1-1-onto→wf1o 4780

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8

This theorem depends on definitions:  df-bi 177  df-an 360  df-f 4791  df-f1 4792  df-f1o 4794

This theorem is referenced by:  f1ofun  5289  f1odm  5290  f1ofveu  5480  isomin  5496  isoini  5497  nenpw1pwlem2  6085