Corollary 2

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

Lie Groups and Lie Algebras, chapter III, § 6. Real and complex Lie groups

Suppose that $\varphi$ is finite-dimensional. For $\varphi$ to be simple (resp. semi-simple), it is necessary and sufficient that $L(\varphi)$ be simple (resp. semi-simple).

This follows from Corollary 1.

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

Cited by

Proposition 22, § 9
Theorem 1, § 9
Lemma 2, § 7

Cites

Corollary 1