In set theory and its applications throughout mathematics, a subclass is a class contained in some other class in the same way that a subset is a set contained in some other set.
[1] In fact, when using a definition of classes that requires them to be first-order definable, it is enough that B be a set; the axiom of specification essentially says that A must then also be a set.
As with subsets, the empty set is a subclass of every class, and any class is a subclass of itself.
Accordingly, the subclass relation makes the collection of all classes into a Boolean lattice, which the subset relation does not do for the collection of all sets.
This set theory-related article is a stub.