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:

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