Definition 2

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

Lie Groups and Lie Algebras, chapter IV, § 2. Tits Systems

A subgroup of $G$ is said to be parabolic if it contains a conjugate of $B$ .

It is clear that every subgroup that contains a parabolic subgroup is parabolic.

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

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Nothing.