What is the proof of the ideal gas law?
The proof? Because real gases at higher temperatures and moderate pressures obey the Ideal Gas Law.
As you know, the Ideal Gas law makes several assumptions that we know are incorrect. Real gas particles have actual volume, and there is also interaction between gaseous particles; facts which the Ideal Gas Law ignores. Nevertheless, the Ideal Gas Law is followed by ALL gases under moderate conditions; even such a gas as
Of course, if we require greater accuracy, we can introduce several parameters that makes the Ideal Gas Law a better fit to reality. The Van der Waals equation is one such attempt.