Lemma 9.8.4 (09GF)—The Stacks project

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Part 1: Preliminaries
Chapter 9: Fields
Section 9.8: Algebraic extensions
Lemma 9.8.4 (cite)

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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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