 The elimination rule is a bit more complicated. Suppose that “\(\theta\) or \(\psi\)” is true. Suppose also that \(\phi\) follows from \(\theta\) and that \(\phi\) follows from \(\psi\). One can reason that if \(\theta\) is true, then \(\phi\) is true. If instead \(\psi\) is true, we still have that \(\phi\) is true. So either way, \(\phi\) must be true.