How do we know that electrons are moving in an electric current?

We are learning about the Hall Effect in high school, but what confused us was that hypothetically if both protons and electrons were moving, but electrons moved much faster, then wouldn't there still be a weaker Hall voltage? How do we experimentally know that only electrons move?

Obviously, since protons are held together with the strong force, it's much more likely that only electrons would move. But how can it be shown experimentally?