Full Idea
Formally, the part-relation is transitive and asymmetric (and thus irreflexive). Hence nothing is a proper part of itself, things aren't proper parts of one another, and if one is part of two which is part of three then one is part of three.
Gist of Idea
The part-relation is transitive and asymmetric (and thus irreflexive)
Source
Peter Simons (Parts [1987], 1.1.1)
Book Reference
Simons,Peter: 'Parts: a Study in Ontology' [OUP 1987], p.10