The real wordsTheory
The law of one price
Law of one priceThe price of an identical good will be the same throughout the world, regardless of which country produces it.
Note what it does not say. It says nothing about the price level of a whole economy, only about one identical good. Applying it to whole price levels is the next step, and it has a different name.
The professor's example runs on steel: American steel at $100 per ton, Japanese steel at 10,000 yen per ton.