The empty set $\empt$ is the unique set such that
\[\forall x : x \notin \empt.\]The existence of $\empt$ is justified by Axiom of Empty Set, Axiom of Existence or Axiom of Infinity. Its uniqueness is justified by Axiom of Extensionality.
The empty set $\empt$ is the unique set such that
\[\forall x : x \notin \empt.\]The existence of $\empt$ is justified by Axiom of Empty Set, Axiom of Existence or Axiom of Infinity. Its uniqueness is justified by Axiom of Extensionality.