Category:Examples of Transitive Classes

This category contains examples of Transitive Class.

Let $A$ denote a class, which can be either a set or a proper class.

Then $A$ is transitive if and only if every element of $A$ is also a subclass of $A$.

That is, $A$ is transitive if and only if:

$x \in A \implies x \subseteq A$

or:

$\forall x: \forall y: \paren {x \in y \land y \in A \implies x \in A}$