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	$$⊢DisjR$$
Assertion	detlem	$$⊢DisjR\leftrightarrow EqvRel\wr R$$

Proof

Step	Hyp	Ref	Expression
1		detlem.1	$$⊢DisjR$$
2		disjim	$$⊢DisjR\to EqvRel\wr R$$
3	1	a1i	$$⊢EqvRel\wr R\to DisjR$$
4	2 3	impbii	$$⊢DisjR\leftrightarrow EqvRel\wr R$$