Intersection ∩
The intersection of two sets (i^i S T) is a set containing the elements that are in both sets.
(=_ (i^i S T) ({} x (/\ (e. x S) (e. x T)))) /edit/peano_new/set_min.ghi/dfin
Properties

Commutative: (=_ (i^i S T) (i^i T S)) /edit/peano_new/set.gh/incom

Associative: (=_ (i^i (i^i S T) U) (i^i S (i^i T U))) /edit/peano_new/set.gh/inass

Idempotent: (=_ (i^i S S) S) /edit/peano_new/set.gh/inidm
Set Theory Overview