  We give a short proof of the "prime-to-$p$ version" of the Manin-Mumford
conjecture for an abelian variety over a number field, when it has
supersingular reduction at a prime dividing $p$, by combining the methods of
Bogomolov, Hrushovski, and Pink-Roessler. Our proof here is quite simple and
short, and neither $p$-adic Hodge theory nor model theory is used. The
observation is that a power of a lift of the Frobenius element at a
supersingular prime acts on the prime-to-$p$ torsion points via nontrivial
homothety.
