 First, observe that if DLiar is not true, then it must be true. If DLiar is not true, then by similar reasoning to what we saw above, we have that the left disjunct of DLiar is true. But a disjunction is true if one of its disjuncts is, so DLiar is true. Thus, if DLiar is not true, it is true and not true, and we have a contradiction. By reductio, then, it must be true; so one of its disjuncts must be true. If it’s the first one, we have a contradiction, so it must be the second one; we can conclude that \(1 = 0\). We have thus proved that \(1 = 0\). Moreover, the sentence ‘\(1 = 0\)’ played no real role in the above reasoning. We could replace it with any other sentence to get a proof of that sentence. 