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Metamath Proof Explorer

Theorem disjimxrnres

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

Ref Expression
Assertion disjimxrnres ⊢ Disj S → Disj R ⋉ S ↾ A

Proof

Step Hyp Ref Expression
1 disjimres ⊢ Disj S → Disj S ↾ A
2 disjimxrn ⊢ Disj S ↾ A → Disj R ⋉ S ↾ A
3 1 2 syl ⊢ Disj S → Disj R ⋉ S ↾ A