Axiom:Axiom of Foundation (Classes)

Axiom

For any non-empty class, there is an element of the class that shares no element with the class.

$\forall X: X \ne \O \implies \exists y: y \in X \land y \cap X = \O$

Also known as

Otherwise known as the Axiom of Regularity.

Sources

• 2010: Elliott Mendelson: Introduction to Mathematical Logic (5th ed.): $4$ Axiomatic Set Theory