Theorem eqvrel1cossinidres

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

	Ref	Expression
Assertion	eqvrel1cossinidres	$$⊢EqvRel\wr \left(R\cap \left({\mathrm{I}\upharpoonright }_A\right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		disjALTVinidres	$$⊢Disj\left(R\cap \left({\mathrm{I}\upharpoonright }_A\right)\right)$$
2	1	disjimi	$$⊢EqvRel\wr \left(R\cap \left({\mathrm{I}\upharpoonright }_A\right)\right)$$