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Solder the adapter onto a short piece of copper pipe, six inches or so. This will give you something you can attach both to the supply lines and to the anti-sweat valve. Attach the pipe and fitting assembly to the valve by using the compression fitting that comes with the valve.
Add a little Teflon tape onto the ends, insert the pipe and slip the compression fitting nut over the pipe. Back it up to the appropriate location over the joint and tighten with a wrench. Next, connect the valve assembly to the water lines by soldering the connections on both the hot and cold water lines at the stop and waste valves.
Connect the 'T' assembly from the hot water line to the mixing valve. Use a compression fitting or solder, which ever you prefer. To make the final connections, secure a pipe onto the remaining port on the mixing valve with a compression fitting. Then, install vent couplings on the other end.
Solder the final joints. Slowly turn on the water at the new stop and waste valves. Start with the cold line, then the hot. Finally, flush the toilet a few times to get the air out of the lines.