Definition 3
Tag 06RZ, permanent. Cite it as [Bourbaki, Tag 06RZ].
Algebra, V, p. 109, § 14. Transcendental extensions
A subset B of an extension E of a field K is a transcendence basis of E (over K) if B is algebraically free over K and E is algebraic over K(B).
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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