Theorem 58: The identity rule (inference rule)

We may (from no premises) infer that any statement \phi entails itself: \cfrac{}{\phi \vdash \phi}.

Proof: Take \phi as an assumption. Using conjunction introduction, we infer that the conjunction \phi \wedge \phi holds. Then, by conjunction elimination, we infer \phi holds. We have now justified the inference that \phi entails \phi . \square