Remark 1
Tag 06SI, permanent. Cite it as [Bourbaki, Tag 06SI].
Algebra, V, p. 112, § 14. Transcendental extensions
If E is a subextension of L which is algebraic over K, then it is algebraically disjoint from every subextension F of L. For an extension of K to be algebraic it is necessary and sufficient that it should be algebraically disjoint from itself.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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