Systems of axioms for elementary logic we can find in textbooks are usually not very transparent; and the reader might well wonder how did precisely such a set of axioms come into being. In this paper we present a way of constituting one such non-transparent set of axioms, namely the one presented by E. Mendelson in his Introduction to Mathematical Logic, in a transparent way, with the aim of helping the reader to get an insight into the workings of the axioms.