Theorem detid

Description: The cosets by the identity relation are in equivalence relation if and only if the identity relation is disjoint. (Contributed by Peter Mazsa, 31-Dec-2021)

	Ref	Expression
Assertion	detid	⊢ ( Disj I ↔ EqvRel ≀ I )

Proof

Step	Hyp	Ref	Expression
1		disjALTVid	⊢ Disj I
2	1	detlem	⊢ ( Disj I ↔ EqvRel ≀ I )