Theorem f1orel 5645

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 5644	. 2 |- ( F : A -1-1-onto-> B -> Fun F )
2		funrel 5397	. 2 |- ( Fun F -> Rel F )
3	1, 2	syl 14	1 |- ( F : A -1-1-onto-> B -> Rel F )

This proof depends on syntax axioms:   -> wi 4   Rel wrel 4781   Fun wfun 5374   -1-1-onto->wf1o 5379

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106

This proof depends on definitions:  df-bi 117  df-fun 5382  df-fn 5383  df-f 5384  df-f1 5385  df-f1o 5387

This theorem is used by:  f1ococnv1  5671  isores1  6023  ssenen  7156  dif1en  7187