  Frege’s system (i.e., his term logic/predicate calculus) consisted of a language and an apparatus for proving statements. The latter consisted of a set of logical axioms (statements considered to be truths of logic) and a set of rules of inference that lay out the conditions under which certain statements of the language may be correctly inferred from others. Frege made a point of showing how every step in a proof of a proposition was justified either in terms of one of the axioms or in terms of one of the rules of inference or justified by a theorem or derived rule that had already been proved.