Theorem f1rel 5255

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 5253	. 2 |- ( F : A -1-1-> B -> F Fn A )
2		fnrel 5146	. 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 4472   Fn wfn 5044   -1-1->wf1 5046

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-fun 5051  df-fn 5052  df-f 5053  df-f1 5054

This theorem is referenced by:  f1dmvrnfibi  6733