Condition for Planes to be Parallel

Theorem
Let $P = \alpha_1 x_1 + \alpha_2 x_2 + \alpha_3 x_3 = \gamma$ be a plane in $\R^3$.

Then the plane $P'$ is parallel to $P$ iff $P'$ is the set of all $\left({x_1, x_2, x_3}\right) \in \R^3$ where:
 * $\exists \gamma' \in \R: \alpha_1 x_1 + \alpha_2 x_2 + \alpha_3 x_3 = \gamma'$