Theorem disjALTVinidres

Description: The intersection with restricted identity relation is disjoint. (Contributed by Peter Mazsa, 31-Dec-2021)

	Ref	Expression
Assertion	disjALTVinidres	$$⊢Disj\left(R\cap \left({\mathrm{I}\upharpoonright }_A\right)\right)$$

Proof

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