The statement is true.

To see, start from any consumption bundle of two goods on a diagram. Now try to find an other bundle that the consumer likes equally as the original one. There are only two possible cases:

1. Suppose you increase the consumption of one good, holding the other one constant. Since both goods are desirable, the consumers must be strictly better off now. To make the consumer like the new bundle only exactly as much as before, we must reduce the consumption of the other good. Hence the new consumption bundle must lie to the southeast of the original bundle.

2.Suppose you decrease the consumption of one good, holding the other one constant. Since both goods are desirable, the consumers must be strictly worse off now. To make the consumer like the new bundle only exactly as much as before, we must increase the consumption of the other good. Hence the new consumption bundle must lie to the northwest of the original bundle.

From 1. and 2. we know that the consumption bundles that consumer are indifferent between are either to the northwest or southeast of any given bundle. Hence, then indifference curve - a curve that connects all such bundles - must be download sloping.