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 |