Description: Alternate definition of relation: a class is a relation if and only if it is equal to its "relation part" (see relpart ). (Contributed by NM, 14-May-2008) Do not depend on df-cnv to move it earlier. (Revised by BJ, 16-Oct-2026)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | bj-dfrel3 | |- ( Rel R <-> ( R |` _V ) = R ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | dfss2 | |- ( R C_ ( _V X. _V ) <-> ( R i^i ( _V X. _V ) ) = R ) |
|
| 2 | df-rel | |- ( Rel R <-> R C_ ( _V X. _V ) ) |
|
| 3 | df-res | |- ( R |` _V ) = ( R i^i ( _V X. _V ) ) |
|
| 4 | 3 | eqeq1i | |- ( ( R |` _V ) = R <-> ( R i^i ( _V X. _V ) ) = R ) |
| 5 | 1 2 4 | 3bitr4i | |- ( Rel R <-> ( R |` _V ) = R ) |