Definition 2

Tag 0DTT, permanent. Cite it as [Bourbaki, Tag 0DTT].

A projective resolution (resp. free, resp. flat) of the $A$ -module $M$ is a left resolution $(P,p)$ of $M$ such that the complex $P$ is projective (resp. free, resp. flat) (X, p. 25). An injective resolution of $M$ is a right resolution $(e,E)$ of $M$ such that the complex $E$ is injective (loc. cit.).

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