What is the work-energy theorem?

I think what you are referreing to is a physical law (not really a theorem). The 1st law of thermodynamics states:

Increase in internal energy of a system = heat supplied to the system - work performed by the system

In physics they typically ignore heat, and so this becomes:

Change in energy + work performed = 0.

The work energy theorem says that ''The work done by the net force acting on a body results change only in its kinetic energy. ''

But if the resultant force is in vertically up direction it will surely change its potential energy too