Reference for the bijection of parabolic subgroups $P$ containing $B$ and subsets of the set of simple roots $\Delta(B)$

Question

Let $G$ be a split reductive group over a perfect field $k$ (not necessarily algebraically closed) with split maximal torus $T$ and Borel $B \supset T$.

Then there is(/should be) an inclusion-preserving bijection from the set of parabolic subgroups $P$ of $G$ containing $B$ to the set of subsets of the set of simple roots $\Delta(B)$ associated to $B$.

Does someone know a (good) reference for this?

I know that this question is more suitable for MathStackExchange but I got the impression, that there is not much activity at the moment.

Answer 1

Gunter Malle and Donna Testerman, Linear algebraic groups and finite groups of Lie type. Cambridge Studies in Advanced Mathematics, 133. Cambridge University Press, Cambridge, 2011.

See Proposition 12.2.