Corollary 2

Tag 00WP, permanent. Cite it as [Bourbaki, Tag 00WP].

Lie Groups and Lie Algebras, chapter VII, § 5. Decomposable linear Lie algebras

The Cartan subalgebras of a decomposable Lie subalgebra of $\mathfrak{g}\mathfrak{l}(V)$ are decomposable.

This follows from Corollary 1.

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.

Cited by

Remark, § 5
Theorem 2, § 5

Cites

Corollary 1