Let's do a proof by contradiction.

Suppose that trueness does not exist. Then proposition A, "Trueness exists", is untrue. In that case, falseness must exist, as a property describing the negative status of proposition A. However, this implies that a proposition B, "The statement 'trueness exists' is false", must now be true. This directly contradicts proposition A.

Therefore, trueness must necessarily exist, for even to conclude that it does not exist immediately verifies its existence.