A downhole valve for use in a well has a closure device that is biased closed to seal against flow through the central bore of the valve. A plurality of pistons are each coupled to a respective hydraulic control line into the valve. Each piston is adapted to reside in an actuated position, supporting the closure open, when at least a specified hydraulic pressure is supplied through its control line, and to reside in an unactuated position, not supporting the closure open, when at least the specified hydraulic pressure is not present in its control line. The valve has a chamber containing a hydraulic fluid hydraulically coupling the pistons to support any piston not receiving the specified hydraulic pressure in an unactuated position. In certain aspects, when the piston is in the unactuated position, it seals against communication of fluid with its respective control line using a static-type seal.