Corollary 1
Tag 0045, permanent. Cite it as [Bourbaki, Tag 0045].
Algebra, VIII, p. 56, § 4. Semisimple Modules
Every module that is the sum of a family of simple modules is semisimple.
It suffices to apply Theorem 1 to the case N = 0.
Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.