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 )