  In analogy with Almgren's Theorem for area minimizing currents of general
dimension and codimension, we prove that an $m$-dimensional semicalibrated
current in a $(n+m)$-dimensional $C^{3,\varepsilon_0}$ manifold, semicalibrated
by a $C^{2,\varepsilon_0}$ $m$-form, has singular set of Hausdorff dimension at
most $m-2$.
