Corollary
Tag 05RL, permanent. Cite it as [Bourbaki, Tag 05RL].
Algebra, chapter II, § 7. Vector spaces
For a subset B of a vector space E, the following properties are equivalent: (a) B is a basis of E. (b) B is a maximal free subset of E. (c) B is a minimal generating system of E. This follows immediately from Theorem 2.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.