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We prove that in Einstein-Maxwell theory the inequality $(8\pi J)^2+(4\piQ^2)^2 < A^2$ holds for any sub-extremal axisymmetric and stationary black holewith arbitrary surrounding matter. Here $J, Q$, and $A$ are angular momentum,electric charge, and horizon area of the black hole, respectively.

A universal inequality for axisymmetric and stationary black holes with surrounding matter in the Einstein-Maxwell theory