  In the Bogoliubov-Fr\"ohlich model, we prove that an impurity immersed in a
Bose-Einstein condensate forms a stable quasi-particle when the total momentum
is less than its mass times the speed of sound. The system thus exhibits
superfluid behavior, as this quasi-particle does not experience friction. We do
not assume any infrared or ultraviolet regularization of the model, which
contains massless excitations and point-like interactions.
