Kurt Gödel was the first to suggest an axiomatization of modal logic based on non-modal classical propositional logic with rules of necessitation. In his one-page 1933 paper, ‘An interpretation of the intuitionistic propositional calculus’, he replaced the necessity symbol by a provability operator, meaning ‘it is provable that,’ and offered a modal translation of Heyting’s intuitionistic logic. He noted that his provability axioms, allowing the assertion of the completeness and consistency of a formal system in which arithmetic can be represented, must fail. With provability interpreted as necessity, his axioms provide S4. Mordchaj Wajsberg’s aim in his 1933 ‘An extended calculus of classes’, a contribution contemporaneous with that of Gödel, was to provide an axiomatic basis for Hilbert and Ackermann’s ‘class calculus.’ In 1927, he had already noted the importance of the axiom first published in Becker’s 1930. In the present work, Wajsberg shows that the axiom allows us not only to reduce all modalities to six, but also to reduce all modal functions to formulae of first degree.