Theorem f1rel 6104

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 6102	. 2 |- ( F : A -1-1-> B -> F Fn A )
2		fnrel 5989	. 2 |- ( F Fn A -> Rel F )
3	1, 2	syl 17	1 |- ( F : A -1-1-> B -> Rel F )

Syntax hints:   -> wi 4   Rel wrel 5119   Fn wfn 5883   -1-1->wf1 5885

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386  df-fun 5890  df-fn 5891  df-f 5892  df-f1 5893

This theorem is referenced by: (None)