Proposition 27
Tag 0AJL, permanent. Cite it as [Bourbaki, Tag 0AJL].
Lie Groups and Lie Algebras, chapter III, § 9. Commutators, centralizers and normalizers in a Lie group
Let G be a finite-dimensional connected real or complex Lie group. The following conditions are equivalent: (i) is simple; (ii) the only normal integral subgroups of G are and G and further G is not commutative. This follows from § 6, no. 6, Proposition 14.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.