In this paper, we generalize two theorems in General Relativity. The symmetry in the conditions for the theorems is relaxed to conformal symmetry. The generalized theorems read as follows: 1. Any conformally spherically symmetric electro-vacuum solution to Einstein equations must be the Reissner-Nordstrom solution. 2. Any conformally plane-symmetric electro-vacuum solution to Einstein equations must be the Kar solution.