We derive a semi-analytical expression for the uplink inter-cell interference (ICI) assuming proportional fair scheduling (with a maximum normalized signal-to-noise ratio (SNR) criterion) deployed in the cellular network. The derived expression can be customized for different models of channel statistics that can capture path loss, shadowing, and fading. Firstly, we derive an expression for the distribution of the locations of the allocated user in a given cell. Then, we derive the distribution and moment generating function of the uplink ICI from one interfering cell. Finally, we determine the moment generating function of the cumulative uplink ICI from all interfering cells. The derived expression is utilized to evaluate important network performance metrics such as outage probability and fairness among users. The accuracy of the derived expressions is verified by comparing the obtained results to Monte Carlo simulations.