Definition:Antisymmetric Relation/Class Theory/Definition 2

Definition
Let $V$ be a basic universe.

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

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

Also known as
Some sources (perhaps erroneously) use this definition for an asymmetric relation.

Also see

 * Equivalence of Definitions of Antisymmetric Relation (Class Theory)