A safety system brake system comprises a hydraulic pressure-providing device having a pressure chamber connected to at least one brake circuit by a separating valve and into which pressure chamber a piston is moved to build up pressure. The pressure chamber is a two-stage pressure chamber having first and second sub-chambers. During pressure build-up the piston is moved into the first and then the second sub-chamber. The two sub-chamber are hydraulically closed off from each other when the piston is moved a specified distance into the second sub-chamber. A first check valve is connected to the first sub-chamber on a suction side and to a brake fluid reservoir on a blocking side. A second check valve is connected to the second sub-chamber on a suction side, and to the suction side of the first check valve on the blocking side.