Theorem f1ofn 5147

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 5146	. 2 |- ( F : A -1-1-onto-> B -> F : A --> B )
2		ffn 5066	. 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 4917   -->wf 4918   -1-1-onto->wf1o 4921

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104

This theorem depends on definitions:  df-bi 115  df-f 4926  df-f1 4927  df-f1o 4929

This theorem is referenced by:  f1ofun  5148  f1odm  5150  isocnv2  5472  isoini  5477  isoselem  5479  bren  6251  en1  6302  phplem4  6341  phplem4on  6353  dif1en  6364  supisolem  6421  ordiso2  6446