  We show that the Bronnikov theorem on the nonexistence of regular
electrically charged black holes can be circumvented. In the frame of nonlinear
electrodynamics, we present the exact regular black hole solutions of a hybrid
type. They are electrically charged, but contain a `dual' core confining a
polarization of magnetic charges.
  The considered example is based on a modification of the Ay\'on-Beato &
Garc\'\i a solution. It represents a very specific realization of the idea on
confinement based on dual electrodynamics and dual superconductivity.
