# Category:Transitive Classes

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This category contains results about 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 3 subcategories, out of 3 total.

## Pages in category "Transitive Classes"

The following 9 pages are in this category, out of 9 total.