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Proper Subset ⊂

The set S is a subset of T if all the elements in S are in T and S is not equal to T.
Proper subset is defined as

(<-> (C. S T) (/\ (C_ S T) (-. (=_ S T)))) /edit/peano_new/set_min.ghi/df-pss

The difference between a subset and a proper subset is that
when the sets are equal they are subset of each other, but not proper subsets.

Set Theory Overview