Definition 1
Tag 05V1, permanent. Cite it as [Bourbaki, Tag 05V1].
Algebra, chapter II, § 8. Restriction of the field ofscalars in vector spaces
Let V be a right vector space over a field K and K' a subfield of K. Every vector sub-K'-space V' of V satisfying the equivalent conditions of Proposition 1 is called a K'-structure on V.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.