Description: The class of identity relations is disjoint. (Contributed by Peter Mazsa, 20-Jun-2021)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | disjALTVid | ⊢ Disj I |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | cosscnvid | ⊢ ≀ ◡ I = I | |
| 2 | 1 | eqimssi | ⊢ ≀ ◡ I ⊆ I |
| 3 | reli | ⊢ Rel I | |
| 4 | dfdisjALTV2 | ⊢ ( Disj I ↔ ( ≀ ◡ I ⊆ I ∧ Rel I ) ) | |
| 5 | 2 3 4 | mpbir2an | ⊢ Disj I |