  We derive two new integral mass formulas for stationary black holes in
Einstein-Yang-Mills theory. From these we derive a formula for $ \J \Omega -Q V
$, from which it follows immediately that any stationary, nonrotating,
uncharged black hole is static and has vanishing electric field on the static
slices. In the Einstein-Maxwell case, we have, in addition, the ``generalized
Smarr mass formula", for which we provide a new, simple derivation. When
combined with the other two formulas, we obtain a simple proof that nonrotating
Einstein-Maxwell black holes must be static and have vanishing magnetic field
on the static slices. Our mass formulas also can be generalized to cases with
other types of matter fields, and we describe the nature of these
generalizations.
