Minimal normal implies pi-group or pi'-group in pi-separable

Statement
Suppose $$\pi$$ is a set of primes and $$G$$ is a finite group that is $$\pi$$-separable (see fact about::pi-separable group). Suppose $$H$$ is a fact about::minimal normal subgroup of $$G$$. Then, $$H$$ is either a $$\pi$$-group (i.e., all prime factors of the order of $$H$$ are in $$\pi$$) or a $$\pi'$$-group (i.e., none of the prime factors of the order of $$H$$ are in $$\pi$$).

Related facts

 * Minimal normal implies central in nilpotent
 * Minimal normal implies elementary abelian in finite solvable