Proposition 1
Tag 06K1, permanent. Cite it as [Bourbaki, Tag 06K1].
Algebra, chapter V, § 7. Separable algebraic extensions
— Let E be an algebraic extension of K. If E is separable, then every subextension of E is separable. Conversely, if every subextension of finite degree of E is separable then E is separable.
This follows immediately from Definition 1.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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