Lower central series of a free group 3

Question

Let $F$ be free group on two generator $x$ and $y$ and $F_i$ be $i$-th component of lower central series of $F$. If $F$ is generated mod $F_1=[F,F]$ by $b_1,...,b_n$ then $F_r$ is generated mod $F_{r+1}$ by elements of the form $[b_i,w]$ with $w \in F_{r-1}$. Where could I find the proof of the above statement?