Full Idea
A set is a 'proper subset' of another set if some things in the large set are not in the smaller set
Gist of Idea
A 'proper subset' is smaller than the containing set
Source
Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.6)
Book Reference
Priest,Graham: 'Introduction to Non-Classical Logic' [CUP 2001], p.-6