Remark 2

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

Commutative Algebra, chapter IX, § 2. Anneaux de Cohen

Let A be a separated and complete local ring, $k$ its residue field and $\pi$ the canonical homomorphism of A onto $k$ . It may be shown that there exists a multiplicative subset S of A (not unique in general) such that $\pi$ induces a bijection of S onto $k$ (cf. p. 72, Exercise 11).

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

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