A Strictly Proper Second-Order Equation Operator is Proper

Let $n\ge1$ be a natural number, let $U\subseteq\mathbb{R}^n$ be an open subset of Euclidean space $\mathbb{R}^n$, let $\mathbb{R}$ be the ordered field of real numbers, and let $F$ be a second-order equation operator on $U$.

If there exists $\gamma\in\mathbb{R}$ with $0<\gamma$ such that $F$ is strictly proper with constant $\gamma$, then $F$ is proper.