We formally prove Liu and Layland's classic theorem on the Rate Monotonic Scheduler in Duration Calculus, a real time interval temporal logic. We describe the assumption of the system, the scheduling policy, the requirement, i.e., service is met for the processes before their deadlines, all by Duration Calculus formulae. That a feasibility condition is sufficient is formalized as logical implication. By using the proof system of Duration Calculus, we formally prove that the feasibility condition due to Liu and Layland is sufficient.