Theorem f1orel 5370

Description: A one-to-one onto mapping is a relation. (Contributed by NM, 13-Dec-2003.)

Assertion

Ref	Expression
f1orel	|- ( F : A -1-1-onto-> B -> Rel F )

Proof of Theorem f1orel

Step	Hyp	Ref	Expression
1		f1ofun 5369	. 2 |- ( F : A -1-1-onto-> B -> Fun F )
2		funrel 5140	. 2 |- ( Fun F -> Rel F )
3	1, 2	syl 14	1 |- ( F : A -1-1-onto-> B -> Rel F )

Syntax hints:   -> wi 4   Rel wrel 4544   Fun wfun 5117   -1-1-onto->wf1o 5122

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-fun 5125  df-fn 5126  df-f 5127  df-f1 5128  df-f1o 5130

This theorem is referenced by:  f1ococnv1  5396  isores1  5715  ssenen  6745  dif1en  6773