对任意转轴都有力矩平衡,则
$\sum \vec{r_i} \times \vec{F_i} = 0$
选取两个平行的转轴,使得
$\vec{r_{i1}} - \vec{r_{i2}} = \Delta \vec r \\ \Delta \vec r \times \vec F_i \ne 0$
则有
$\sum \vec{r_{i1}} \times \vec{F_i} = 0 \\ \sum\vec{r_{i2}} \times \vec{F_i} = 0$
联立得
$\sum (\vec{r_{i1}}-\vec{r_{i2}}) \times \vec{F_i} = 0 \\ \Delta \vec r \times \sum\vec{F_i} = 0$
则必有
$\vec{F_i}=0$