  We show that the area-angular momentum-charge inequality (A/(4\pi))^2 \geq
(2J)^2 + (Q_E^2 + Q_M^2)^2 holds for apparent horizons of electrically and
magnetically charged rotating black holes in generic dynamical and non-vacuum
spacetimes. More specifically, this quasi-local inequality applies to axially
symmetric closed outermost stably marginally (outer) trapped surfaces, embedded
in non-necessarily axisymmetric black hole spacetimes with non-negative
cosmological constant and matter content satisfying the dominant energy
condition.
