Theorem disjALTVxrnidres

Description: The class of range Cartesian product with restricted identity relation is disjoint. (Contributed by Peter Mazsa, 25-Jun-2020) (Revised by Peter Mazsa, 27-Sep-2021)

	Ref	Expression
Assertion	disjALTVxrnidres	$$⊢DisjR⋉\left({\mathrm{I}\upharpoonright }_A\right)$$

Proof

Step	Hyp	Ref	Expression
1		disjALTVid	$$⊢Disj\mathrm{I}$$
2		disjimxrnres	$$⊢Disj\mathrm{I}\to DisjR⋉\left({\mathrm{I}\upharpoonright }_A\right)$$
3	1 2	ax-mp	$$⊢DisjR⋉\left({\mathrm{I}\upharpoonright }_A\right)$$