Symmetricity in Kaiming initialization

Question

Kaiming initialization paper says that "If we let $w_{l-1}$ have a symmetric distribution around zero and $b_{l-1 } = 0$, then $y_{l-1}$ has zero mean and has a symmetric distribution around zero". Can someone explain how symmetricity of $w_{l-1}$ leads to symmetricity of $y_{l-1}$ ? A mathematical proof would be great.