 Just as, in axiomatic formulations of logic (“Frege systems” or “Hilbert-style” systems), different choices of axioms are possible for a particular logic, different sets of rules can be chosen in formulating a natural deduction system. In particular, one or more rules of supposition can, in the presence of others, be replaced by inference rules. Thus, for example, it is possible to have  \(\rightarrow\)-I[14]as  the only rule of supposition, any others being replaced by inference rules having, among their premisses, conditionals summarizing the subproofs of the original rules. (Elementary students may find it easier to learn inference rules than to learn suppositional rules, in which case this sort of system may be a rational choice for elementary textbooks.) Alternatively, \(\neg\)-I may be taken as the only rule of supposition, \(\rightarrow\)-I being replaced by a rule allowing \((A\rightarrow B)\) to be inferred from \(\neg(A\land\neg B)\). Other choices are also possible. D’Agostino, Gabbay, and Modgil (2020) present a very elegant system for Classical propositional logic in which the only rule of supposition is an “excluded middle” rule: a formula may be asserted if it is derived in each of a pair of subproofs, the hypothesis of one being the negation of the hypothesis of the other.