A surface-current equivalence theorem that states that the electromagnetic fields outside a three-dimensional (3-D) source region can be generated (to any degree of accuracy) by electric and magnetic surface currents that lie in a single plane within the source region is proven by showing that the fields of each spherical electromagnetic multipole can be generated by delta-function electric and magnetic surface currents in an arbitrarily oriented plane of infinitesimal area located at the origin of the spherical multipole. The theorem can be used to justify integral equation methods based on equivalent surface currents to represent radiated and scattered fields. Application of the theorem to antennas reveals that the output of an arbitrary linear receiving antenna can be expressed in terms of just the transverse spatial derivatives of the transverse components of the incident electric and magnetic fields at a single point in space. The coefficients of the transverse linear differential operator are expressed in terms of the spherical multipole coefficients of the antenna's complex receiving pattern.