Waveguide H field boundary condition

Corneo

When solving for the TE field solutions in a rectangular waveguide, the boundary condition [tex]\frac{\partial H_z}{\partial x}\bigg|_{x=0,a} = 0[/tex] is used. Where does that come from? Can you get this from the [tex]\hat n \times [\bar H_1 - \bar H_2] = 0[/tex] or the one for B-fields? Thank you.