Abstract: A system for dispensing a mixture of a first product and a second product has a pump which presents a pump body that is intended to be connected to a bottle which contains the first product. The pump has a piston secured to a push button so as to be actuated in translatory motion in the body. The piston defines within the body a dosing chamber having a feeding inlet formed on a lower part of the body. The pump further has a lower check valve that is slidingly mounted in the dosing chamber between an upper opening position and a lower closing position of the feeding inlet.