Millimeter wave (mmWave) cellular systems will enable gigabit-per-second data rates due to the large bandwidth available at mmWave frequencies. Thanks to the small wavelength corresponding to the mmWave frequencies, mmWave systems can benefit from exploiting large antenna arrays at both transmitter and receiver. Although highly directional beamforming has been envisioned to play a key role to realize sufficient link margin, it is also possible to use these large arrays in other ways. For example, a hybrid array architecture can be exploited to either cancel or null an interferer. In this paper we analyse the effect of interference cancellation in downlink mmWave communications. We exploit partial zero forcing (PZF) at the user in order to cancel the interference from a set of interfering base stations (BSs) and derive closed form expression for the probability of coverage. Simulation results show that as the density of base stations increases, interference mitigation through partial zero forcing enhances the probability of coverage implying the necessity of interference mitigation in dense mmWave networks.