Corollary 1
Tag 06S7, permanent. Cite it as [Bourbaki, Tag 06S7].
Algebra, chapter V, § 14. Transcendental extensions
— Let S be a subset of E such that E is algebraic over K(S). Then Card(S) ≥ n; if the cardinal of S is equal to n, then S is algebraically free over K (hence it is then a transcendence basis of E 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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