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This paper is concerned with the axioms of Hilbert and Bernays for the propositional calculus (5071, p. 66). To establish the independence of these axioms, Hilbert and Bernays use in two cases (axioms 1.1 and 1.3) tables which involve as many as four truth-values. Wang shows that the independence of 1.1 can be established by a table involving only three truth-values. The reviewer would add that the like is true of 1.3 (Wang's statement to the contrary notwithstanding), the following table being sufficient for the purpose, with 1 as the designated truth-value