Corollary 3

Tag 06S9, permanent. Cite it as [Bourbaki, Tag 06S9].

Algebra, chapter V, § 14. Transcendental extensions

— Every subset of $E$ which is algebraically free over $K$ has at most $n$ elements, and if it has exactly $n$ elements, it is 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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