# Category:Transitive Classes

This category contains results about Transitive Classes.
Definitions specific to this category can be found in Definitions/Transitive Classes.

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:

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

## Subcategories

This category has the following 8 subcategories, out of 8 total.

## Pages in category "Transitive Classes"

The following 18 pages are in this category, out of 18 total.