First Officer reported both EDHP #1 and EDHP #2 failed during flight and hydraulic system A lost all fluid. The flight crew was able to continue to the destination airport.

Narrative

During cruise at FL 360 the #1 EDHP (Engine Driven Hydraulic Pump) Low-Pressure Annunciator illuminated and the corresponding QRH procedure was executed. Shortly after the Low-Pressure Annunciator; the A System hydraulic quantity decreased to 20% initially and then stabilized at a 9-12% quantity indication. Dispatch and Maintenance were advised via ACARS. Maintenance informed Crew that based on the information we were providing; the aircraft would likely lose the A Hydraulic System in it's entirety. Shortly thereafter; the #2 EDHP Low-Pressure Annunciator illuminated for approximately two to three minutes. Because the System B was indicating 106% quantity and pressure was within normal operating ranges; we waited to turn off the #2 EDHP to assess the situation; as we had now received a low pressure indication on both the A and B System EDHP. During that brief assessment period the Low Pressure Annunciator light on the #2 EDHP extinguished and pressure and quantity remained within the normal range for the duration of the flight. Based on the remaining low-pressure and quantity of the A System Hydraulics; a [request for priority handling] was made; QRH was executed and an uneventful landing was completed.