According to the Ideal Gas Equation, $pV = nRT$ . Let the number of moles of the first gas be $n_1 = \frac{PV}{RT}$ and the second gas be $n_2 = \frac{PV}{RT}$. When mixed in the same volume $V$ and at the same temperature $T$, the total number of moles is $n_{total} = n_1 + n_2 = \frac{2PV}{RT}$. The pressure of the mixture is $P_{mix} = \frac{n_{total}RT}{V} = \frac{(2PV/RT)RT}{V} = 2P$. Alternatively, according to Dalton's Law of Partial Pressures, the total pressure is the sum of the individual partial pressures exerted by the gases . Since V and T are constant, each gas exerts a partial pressure P, so $P_{total} = P + P = 2P$.