Description: The cosets by the restricted identity relation are in equivalence relation if and only if the restricted identity relation is disjoint. (Contributed by Peter Mazsa, 31-Dec-2021)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | detidres | |- ( Disj ( _I |` A ) <-> EqvRel ,~ ( _I |` A ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | disjALTVidres | |- Disj ( _I |` A ) |
|
| 2 | 1 | detlem | |- ( Disj ( _I |` A ) <-> EqvRel ,~ ( _I |` A ) ) |