Theorem f1fun 5232

Description: A one-to-one mapping is a function. (Contributed by NM, 8-Mar-2014.)

Assertion

Ref	Expression
f1fun	|- ( F : A -1-1-> B -> Fun F )

Proof of Theorem f1fun

Step	Hyp	Ref	Expression
1		f1fn 5231	. 2 |- ( F : A -1-1-> B -> F Fn A )
2		fnfun 5124	. 2 |- ( F Fn A -> Fun F )
3	1, 2	syl 14	1 |- ( F : A -1-1-> B -> Fun F )

Syntax hints:   -> wi 4   Fun wfun 5022   Fn wfn 5023   -1-1->wf1 5025

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105

This theorem depends on definitions:  df-bi 116  df-fn 5031  df-f 5032  df-f1 5033

This theorem is referenced by:  f1cocnv2  5294  f1o2ndf1  6007  f1dmvrnfibi  6707  djuinj  6841