Theorem f1ofun 5148

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 5147	. 2 |- ( F : A -1-1-onto-> B -> F Fn A )
2		fnfun 5016	. 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 4916   Fn wfn 4917   -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-fn 4925  df-f 4926  df-f1 4927  df-f1o 4929

This theorem is referenced by:  f1orel  5149  f1oresrab  5350  isose  5480  f1opw  5727  xpcomco  6323  f1dmvrnfibi  6393