Theorem disjimxrn

Description: Disjointness condition for range Cartesian product. (Contributed by Peter Mazsa, 15-Dec-2020) (Revised by Peter Mazsa, 22-Sep-2021)

	Ref	Expression
Assertion	disjimxrn	⊢ ( Disj 𝑆 → Disj ( 𝑅 ⋉ 𝑆 ) )

Proof

Step	Hyp	Ref	Expression
1		disjorimxrn	⊢ ( ( Disj 𝑅 ∨ Disj 𝑆 ) → Disj ( 𝑅 ⋉ 𝑆 ) )
2	1	olcs	⊢ ( Disj 𝑆 → Disj ( 𝑅 ⋉ 𝑆 ) )