Definition:Antisymmetric Relation/Class Theory/Definition 1

Definition
Let $V$ be a basic universe.

Let $\RR \subseteq V \times V$ be a relation in $V$.

$\RR$ is antisymmetric :
 * $\tuple {x, y} \in \RR \land \tuple {y, x} \in \RR \implies x = y$

that is:
 * $\set {\tuple {x, y}, \tuple {y, x} } \subseteq \RR \implies x = y$

Also see

 * Equivalence of Definitions of Antisymmetric Relation (Class Theory)