Corollary 2

Tag 05LV, permanent. Cite it as [Bourbaki, Tag 05LV].

Algebra, chapter II, § 1. Modules

If a module E admits an infinite basis B, every generating system of E has cardinal \geq Card(B) and every basis of E is equipotent to B.

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

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Nothing.