  From the axiomatic \(p \vdash p\) (anything follows from itself) we deduce that \(p\) follows from \(p\) together with \(q\), and then by residuation, \(p \vdash q \rightarrow p\). If we wish to reject the inference from \(p\) to \(q \rightarrow p\), then we either reject residuation, or reject the identity axiom at the start of the proof, or we reject the first step of the proof. It is illuminating to consider what is involved in this last option. Here, we are to deny that \(p\) follows from \(p, q\). In general, we are to reject the inference rule that has this form: 