Definition:Minimal Element/Definition 2

Definition
Let $\left({S, \preceq}\right)$ be an ordered set.

Let $T \subseteq S$ be a subset of $S$.

An element $x \in T$ is a minimal element of $T$ :
 * $\neg \exists y \in T: y \prec x$

where $y \prec x$ denotes that $y \preceq x \land y \ne x$.

Also see

 * Equivalence of Definitions of Minimal Element