Terminology 54: We will state inference rules (or just rules), each taking as premises finitely many inferences of one of the forms \vdash \phi \hspace{5mm} \textup{or} \hspace{5mm} \phi \vdash \psi (i.e. that a statement \phi holds or entails another statement \psi ), yielding one such inference as the conclusion. We may express this using the notation \cfrac{\textup{First premise} \quad \textup{Second premise} \quad \cdots \quad \textup{Final premise}}{\textup{Conclusion}} A few inference rules will be declared; we accept that if each premise of such a rule is justified or is of the form \vdash \phi where \phi is an assumption, then the given conclusion is justified. Further rules will be verified using these rules.