In two commodity worlds if one good is inferior then the other must be

If a good is inferior, then the consumer buys more of it when their income decreases, and less when their income increases.

Let's think about the scenario given. The consumer has two goods available, and when their income decreases, they buy more of both goods. How is this possible? The consumer's budget set has shrunk, so the total value of what they buy must go down, but we're predicting that consumption of each good goes up. We therefore must conclude that it is impossible for both goods to be inferior.