I would like to prove that having two planes
$ax+by+cz+d_1 = 0 \quad\text{and}\quad ax+by+cz+d_2 = 0$
you can automatically have a plane with equal distance from each plane that looks like this:
$ax+by+cz+\frac{d_1+d_2}{2}=0.$
I have tried deriving this from the formula for the distance of a point to a plane, but with no success. Any suggestions?