Corollary 1
Tag 0573, permanent. Cite it as [Bourbaki, Tag 0573].
Algebra, chapter I, § 2. Identity element; cancellable elements; invertible elements
Let E be a monoid, X a subset of E and X' the centralizer of X. The inverse of every invertible element of X' belongs to X'.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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