Theorem f1ofn 5127

Description: A one-to-one onto mapping is function on its domain. (Contributed by NM, 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 5126	. 2 |- ( F : A -1-1-onto-> B -> F : A --> B )
2		ffn 5046	. 2 |- ( F : A --> B -> F Fn A )
3	1, 2	syl 14	1 |- ( F : A -1-1-onto-> B -> F Fn A )

Syntax hints:   -> wi 4   Fn wfn 4897   -->wf 4898   -1-1-onto->wf1o 4901

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99

This theorem depends on definitions:  df-bi 110  df-f 4906  df-f1 4907  df-f1o 4909

This theorem is referenced by:  f1ofun  5128  f1odm  5130  isocnv2  5452  isoini  5457  isoselem  5459  bren  6228  en1  6279  phplem4  6318  phplem4on  6329  dif1en  6337  ordiso2  6357