Full Idea
ZFC is a theory concerned only with sets. Even the elements of all of the sets studied in ZFC are also sets (whose elements are also sets, and so on). This rests on one clearly pure set, the empty set Φ. ..Mathematics only needs pure sets.
Clarification
ZFC abbreviates 'Zermelo-Fraenkel with Choice'
Gist of Idea
Even the elements of sets in ZFC are sets, resting on the pure empty set
Source
A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3)
Book Reference
George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.48
A Reaction
This makes ZFC a much more metaphysically comfortable way to think about sets, because it can be viewed entirely formally. It is rather hard to disentangle a chair from the singleton set of that chair.