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	⊢ Disj ( 𝑅 ⋉ ( I ↾ 𝐴 ) )

Proof

Step	Hyp	Ref	Expression
1		disjALTVid	⊢ Disj I
2		disjimxrnres	⊢ ( Disj I → Disj ( 𝑅 ⋉ ( I ↾ 𝐴 ) ) )
3	1 2	ax-mp	⊢ Disj ( 𝑅 ⋉ ( I ↾ 𝐴 ) )