Remark K657
on D289: Antisymmetric binary relation

Proof technique: establishing an equality by applying antisymmetry

Let $R$ be an [[[d,289]]] on $X \neq \emptyset$ and let $x, y \in X$ each be a [[[d,2218]]] in $X$. If one was interested in establishing the equality $x = y$ then, due to antisymmetry, it is sufficient to prove that $(x, y) \in R$ and $(y, x) \in R$ since this would imply $x = y$.