Finite Subsets form Directed Set

Theorem

Let $I$ be a set.

Denote with $\FF$ the set of finite subsets of $I$.

Let $\subseteq$ be the subset relation on $\FF$.

Then $\struct {\FF, \subseteq}$ is a directed set.

Proof

A fortiori from Finite Subsets form Directed Ordering.

$\blacksquare$