Definition 3
Tag 0AJM, permanent. Cite it as [Bourbaki, Tag 0AJM].
Lie Groups and Lie Algebras, chapter III, § 9. Commutators, centralizers and normalizers in a Lie group
A connected real or complex Lie group is called almost simple if it is finite-dimensional and satisfies the conditions of Proposition 27.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.