Definition 4
Tag 06S6, permanent. Cite it as [Bourbaki, Tag 06S6].
Algebra, chapter V, § 14. Transcendental extensions
— Let E be an extension of a field K. The cardinal of every transcendence basis of E over K is called the transcendence degree of E over K and written tr. deg_K E.
Th. 2 and 3 and Def. 4 imply the following corollaries, where E denotes an extension of a field K, of finite transcendence degree n.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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