Continuing with that principle.

If you know the position of the transmitter and how far away you are from it, you can describe your position as somewhere on a sphere of a radius which is the distance from that transmitter.

If you know the position and distance from a second GPS transmitter, you can describe your position as somewhere on that sphere too. But the two spheres will intersect (the intersection is described by a circle) and so you must be located on the intersection.

If you know the position and distance from a third GPS transmitter, you can describe your position as somewhere on that sphere too. But the three spheres will intersect at only two points!

Knowing that you are located somewhere on a fourth sphere (the earth) one of those two positions will be silly. And so you have fixed your position. In fact an additional measurement is necessary to remove any clock errors and further redings are used to remove other errors caused by the atmophere, etc.