Theorem f1fun 5406

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 5405	. 2 |- ( F : A -1-1-> B -> F Fn A )
2		fnfun 5295	. 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 5192   Fn wfn 5193   -1-1->wf1 5195

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

This theorem depends on definitions:  df-bi 116  df-fn 5201  df-f 5202  df-f1 5203

This theorem is referenced by:  f1cocnv2  5470  f1o2ndf1  6207  f1dmvrnfibi  6921  djuinj  7083