The city supply and tank supply are handled via check valves in the piping itself. The valves are used for winterizing the trailer. One valve should go to your fresh water tank. The other valve will be to an open ended tube/hose or city water hookup and is meant to put into a bottle of RV antifreeze. To winterize you close the valve going to the fresh water tank and open the valve to the antifreeze. You then use the pump to pump antifreeze through the trailer plumbing. It is hard to tell from the picture which is which. Going out on a limb and taking a guess the one you labeled as city is the antifreeze line so would only be opened when winterizing.