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Metamath Proof Explorer

Theorem disjiminres

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

Ref Expression
Assertion disjiminres ⊢ Disj S → Disj R ∩ S ↾ A

Proof

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