Definition of a covering space and uniqueness of a based lift

Define a covering space. Let \[ p:(E,e_0)\to(X,x_0) \] be a covering map and let \[ f:(Y,y_0)\to(X,x_0) \] be continuous, where \(Y\) is path-connected. Prove that there is at most one based lift \[ \widetilde f:(Y,y_0)\to(E,e_0) \] satisfying \[ p\circ\widetilde f=f. \]