 Let \(\theta, \neg \theta\) be a pair of contradictory opposites, and let \(\psi\) be any sentence at all. By (As) we have \(\{\theta, \neg \theta, \neg \psi \}\vdash \theta\) and \(\{\theta, \neg \theta, \neg \psi \}\vdash \neg \theta\). So by \((\neg\)I), \(\{\theta, \neg \theta \}\vdash \neg \neg \psi\). So, by (DNE) we have \(\{\theta , \neg \theta \}\vdash \psi\) . That is, anything at all follows from a pair of contradictory opposites. Some logicians introduce a rule to codify a similar inference: