 The case of \(\phi \rightarrow \psi\) is a little subtler. She will probably want to start by assuming \(\phi\) in order to deduce \(\psi\); but there is some risk of confusion because the sentences that she has written down so far are all of them things to be proved, and \(\phi\) is not a thing to be proved. The examiner can help her by saying ‘I’ll assume \(\phi\), and let’s see if you can get to \(\psi\) from there’. At this point there is a chance that she sees a way of getting to \(\psi\) by deducing a contradiction from \(\phi\); so she may turn the tables on the examiner and invite him to show that his assumption is consistent, with a view to proving that it isn’t. The symmetry is not perfect: he was asking her to show that a sentence is true everywhere, while she is inviting him to show that a sentence is true somewhere. Nevertheless we can see a sort of duality.