Theorem eqvrel1cossxrnidres

Description: The cosets by a range Cartesian product with a restricted identity relation are in equivalence relation. (Contributed by Peter Mazsa, 31-Dec-2021)

	Ref	Expression
Assertion	eqvrel1cossxrnidres	$$⊢EqvRel\wr R⋉\left({\mathrm{I}\upharpoonright }_A\right)$$

Proof

Step	Hyp	Ref	Expression
1		disjALTVxrnidres	$$⊢DisjR⋉\left({\mathrm{I}\upharpoonright }_A\right)$$
2	1	disjimi	$$⊢EqvRel\wr R⋉\left({\mathrm{I}\upharpoonright }_A\right)$$