Corollary 2
Tag 055X, permanent. Cite it as [Bourbaki, Tag 055X].
Algebra, chapter I, § 1. Laws of composition; associativity; commutativity
If all pairs of elements of a subset X are permutable under an associative law T, the law induced by T on the stable subset generated by X is associative and commutative.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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