Interference rejection combiners (IRCs) are very popular in 4G/5G systems. In particular, they are often times used in co-ordinated multi-point (CoMP) networks where the antennas of a neighboring cell's base station (BS) are used in an IRC receiver, in conjunction with the antennas of the BS of a cell-edge UE's own cell, to improve the IRC-SINR of a cell-edge user. But does the IRC-SINR always increase with an increase in the number of antennas? In this paper, we attempt to answer the question theoretically. We give a theoretical derivation that quantifies the improvement in the IRC-SINR when the number of antennas increases by unity. We show that this improvement in IRC-SINR is always greater than or equal to zero. Thus we prove that increasing the number of antennas even by unity will always improve the IRC-SINR. Selecting the extra antennas of the neighbouring cell can be viewed as a special case of antenna selection described in [1]. We also present the IRC-SINR improvement in an uplink CoMP scenario by simulations and verify that it indeed matches with the theoretical gains derived in this paper.