Let $G$ be a reductive group over $\mathbb{Q}$ and let $P_0$ minimal parabolic subgroup.

If $P_1=M_{1}N_{1} \subset P_2=M_2N_2$ are standard parabloic subgroups of $G$, then can we decompose $P_1=(P_1 \cap M_2 )N_2$? It seems it does hold but I don't know why it holds.

Any comments are welcome!