There are two aspects to a proof. The first is theoretical in which we develop a model of how things work based on some fundamental assumptions and deductive logic. To be valid a theoretical statement must have some predictive power AND be confirmed by experiment. When you say "proved physically" it is the experiment described above that confirms the theoretical assertion. This is how science and engineering work.
The above assertion by kubeek is for an ideal transformer with no losses. In the actual experiment the power out will always less than the power in. As an additional confirmation you can measure the temperature of the transformer before applying input power and then measuring the temperature after it has been supplying power to a load for a while. The generation of heat is one reason why the output power is always less than the input power.