sounds like RO water. the sediment filter is what is usually in cartridge 1, carbon block in 2, RO membrane 3rd, then the DI resin (if applicable). so id say as long as there is no weird additives, yes its safe.
I would get a di filter if you don't have one it removes the rest of the impurities that get by. There like 40 bucks at dr foster and smith and easy to hook up.