The proof supplied by O'Brien consists in showing that in a two-good, two-country model, an increase in country A's demand for country B's export raises the relative price of B's export compared to A's export, that is, the terms of trade shift in favor of B. If both countries are specialized in the production of their own export, the domestic price level of A falls and the domestic price level of B rises. So much for the idea that domestic price levels are fixed by convertibility.