The sentential calculiR, under discussion, are axiomatizable and implication is among their primitive terms. The modus ponens and the rule of substitution are their primitive rules. ByS r is denoted the set of sentences obtained from the formulae of the calculusR by substituting sentences of a given language for all variables. The variablesx, y, z ... represent the elements of the setS r , the variablesX, Y, Z ... represent the subsets ofS R . The formulacxy designates an implication withx (...) as its antecedent andy as its consequent,cxy is always an element ofS R δ(X) means, thatX is closed with respect to the modus ponens rule.A R designates the class of allS R -substitutions of the axioms of the sentential calculusR. (shrink)