Description: Equivalent expressions for an element of the relations class. (Contributed by Peter Mazsa, 21-Jul-2021)
Ref | Expression | ||
---|---|---|---|
Assertion | elrels5 | |- ( R e. V -> ( R e. Rels <-> ( R |` dom R ) = R ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elrelsrel | |- ( R e. V -> ( R e. Rels <-> Rel R ) ) |
|
2 | dfrel5 | |- ( Rel R <-> ( R |` dom R ) = R ) |
|
3 | 1 2 | bitrdi | |- ( R e. V -> ( R e. Rels <-> ( R |` dom R ) = R ) ) |