Theorem detlem

Description: If a relation is disjoint, then it is equivalent to the equivalent cosets of the relation, inference version. (Contributed by Peter Mazsa, 30-Sep-2021)

	Ref	Expression
Hypothesis	detlem.1	|- Disj R
Assertion	detlem	|- ( Disj R <-> EqvRel ,~ R )

Proof

Step	Hyp	Ref	Expression
1		detlem.1	|- Disj R
2		disjim	|- ( Disj R -> EqvRel ,~ R )
3	1	a1i	|- ( EqvRel ,~ R -> Disj R )
4	2 3	impbii	|- ( Disj R <-> EqvRel ,~ R )