Theorem disjALTVinidres

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

	Ref	Expression
Assertion	disjALTVinidres	⊢ Disj ( 𝑅 ∩ ( I ↾ 𝐴 ) )

Proof

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