Theorem elrelsrel

Description: The element of the relations class ( df-rels ) and the relation predicate are the same when R is a set. (Contributed by Peter Mazsa, 24-Nov-2018)

	Ref	Expression
Assertion	elrelsrel	|- ( R e. V -> ( R e. Rels <-> Rel R ) )

Proof

Step	Hyp	Ref	Expression
1		elrels2	|- ( R e. V -> ( R e. Rels <-> R C_ ( _V X. _V ) ) )
2		df-rel	|- ( Rel R <-> R C_ ( _V X. _V ) )
3	1 2	bitr4di	|- ( R e. V -> ( R e. Rels <-> Rel R ) )