Corollary
Tag 06RW, permanent. Cite it as [Bourbaki, Tag 06RW].
Algebra, chapter V, § 14. Transcendental extensions
— Let E be an extension of a field K and S a subset of E which is algebraically free over K. If x \in E is transcendental over K(S), then S U {x} is algebraically free over K.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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