In either case, if X is the class or set it being a unit or singleton can be expressed thus: (Ey)(yeX & (z)(zeX --> z=y)) i.e. X contains an element and whatever is element of X is identical to that element.

Intuitively, a unit class is not the same as the individual that is its only element, and this is also the case in standard set theory, though not in some of Quine's systems for set theory and mathematics.

And indeed, if one considers a domain in which there are only classes or sets, one must make do with unit classes or singleton sets as stand-ins for individuals.