Theorem detidres

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

	Ref	Expression
Assertion	detidres	$$⊢Disj\left({\mathrm{I}\upharpoonright }_A\right)\leftrightarrow EqvRel\wr \left({\mathrm{I}\upharpoonright }_A\right)$$

Proof

Step	Hyp	Ref	Expression
1		disjALTVidres	$$⊢Disj\left({\mathrm{I}\upharpoonright }_A\right)$$
2	1	detlem	$$⊢Disj\left({\mathrm{I}\upharpoonright }_A\right)\leftrightarrow EqvRel\wr \left({\mathrm{I}\upharpoonright }_A\right)$$