Description: Intersection with the converse epsilon relation restricted to the quotient set of an equivalence relation is disjoint. (Contributed by Peter Mazsa, 30-May-2020) (Revised by Peter Mazsa, 31-Dec-2021)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | eqvreldisj4 | |- ( EqvRel R -> Disj ( S i^i ( `' _E |` ( B /. R ) ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | eqvreldisj3 | |- ( EqvRel R -> Disj ( `' _E |` ( B /. R ) ) ) |
|
| 2 | disjimin | |- ( Disj ( `' _E |` ( B /. R ) ) -> Disj ( S i^i ( `' _E |` ( B /. R ) ) ) ) |
|
| 3 | 1 2 | syl | |- ( EqvRel R -> Disj ( S i^i ( `' _E |` ( B /. R ) ) ) ) |