Theorem disjimxrnres

Description: Disjointness condition for range Cartesian product with restriction. (Contributed by Peter Mazsa, 27-Sep-2021)

	Ref	Expression
Assertion	disjimxrnres	$$⊢DisjS\to DisjR⋉\left({S\upharpoonright }_A\right)$$

Proof

Step	Hyp	Ref	Expression
1		disjimres	$$⊢DisjS\to Disj\left({S\upharpoonright }_A\right)$$
2		disjimxrn	$$⊢Disj\left({S\upharpoonright }_A\right)\to DisjR⋉\left({S\upharpoonright }_A\right)$$
3	1 2	syl	$$⊢DisjS\to DisjR⋉\left({S\upharpoonright }_A\right)$$