<https://physics.stackexchange.com/a/199976/170242>

In this answer (in the link), it is mentioned that "the internal energy of an ideal gas is independent of volume when considered as a function of volume and temperature."

Later, it is also mentioned that $$\left(\dfrac{\partial U}{\partial X}\right)\_T=0$$ for any variable $X$.

From this, it is easy to conclude that internal energy of an ideal gas is a function of temperature only.

But, can one derive this expression mathematically ?