\section{Properties of Algebraic Extensions}

\begin{theorem}[Algebraic over Algebraic Is Algebraic]
	If $\K$ is an algebraic extension of $\E$ and $\E$ is an algebraic extension of $\F$, then $\K$ is an algebraic extension of $\F$.
\end{theorem}

\begin{corollary}[Subfield of Algebraic Elements]
	Let $\E$ be an extension field of the field $\F$. Then the set of all elements of $\E$ that are algebraic over $\F$ is a subfield of $\E$.
\end{corollary}