Remark 1

Tag 0D91, permanent. Cite it as [Bourbaki, Tag 0D91].

Commutative Algebra, chapter X, § 7. Algèbres lisses

Let $k$ be a field. Every étale $k$ -algebra (A, V, p. 28, def. 1) is formally smooth (loc. cit., p. 34, th. 4, d) and No. 2, prop. 3, b)).

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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