Let $[a, b] \subseteq \mathbb{R}$ be a D544: Closed real interval such that

(i)	\begin{equation} [a, b] \neq \emptyset \end{equation}
(ii)	$f : [a, b] \to \mathbb{R}$ is a D5231: Standard-continuous real function on $[a, b]$

Then \begin{equation} \exists \, m, M \in [a, b] : \forall \, x \in [a, b] : f(m) \leq f(x) \leq f(M) \end{equation}