Lemma 9.8.4. Let $K/E/F$ be a tower of field extensions.

If $\alpha \in K$ is algebraic over $F$, then $\alpha $ is algebraic over $E$.

if $K$ is algebraic over $F$, then $K$ is algebraic over $E$.

Lemma 9.8.4. Let $K/E/F$ be a tower of field extensions.

If $\alpha \in K$ is algebraic over $F$, then $\alpha $ is algebraic over $E$.

if $K$ is algebraic over $F$, then $K$ is algebraic over $E$.

**Proof.**
This is immediate from the definitions.
$\square$

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