Theorem f1rel 5115

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

Assertion

Ref	Expression
f1rel	|- ( F : A -1-1-> B -> Rel F )

Proof of Theorem f1rel

Step	Hyp	Ref	Expression
1		f1fn 5113	. 2 |- ( F : A -1-1-> B -> F Fn A )
2		fnrel 5017	. 2 |- ( F Fn A -> Rel F )
3	1, 2	syl 14	1 |- ( F : A -1-1-> B -> Rel F )

Syntax hints:   -> wi 4   Rel wrel 4368   Fn wfn 4917   -1-1->wf1 4919

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-fun 4924  df-fn 4925  df-f 4926  df-f1 4927

This theorem is referenced by:  f1dmvrnfibi  6393