Theorem f1ofun 5128

Description: A one-to-one onto mapping is a function. (Contributed by NM, 12-Dec-2003.)

Assertion

Ref	Expression
f1ofun	|- ( F : A -1-1-onto-> B -> Fun F )

Proof of Theorem f1ofun

Step	Hyp	Ref	Expression
1		f1ofn 5127	. 2 |- ( F : A -1-1-onto-> B -> F Fn A )
2		fnfun 4996	. 2 |- ( F Fn A -> Fun F )
3	1, 2	syl 14	1 |- ( F : A -1-1-onto-> B -> Fun F )

Syntax hints:   -> wi 4   Fun wfun 4896   Fn wfn 4897   -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-fn 4905  df-f 4906  df-f1 4907  df-f1o 4909

This theorem is referenced by:  f1orel  5129  f1oresrab  5329  isose  5460  f1opw  5707  xpcomco  6300