  To simplify the notation he used the same letter, say \(v\), for some when there were several universal premises, an incorrect step if one accepts Boole’s claim that it is not necessary to eliminate the \(v\)’s immediately. Distinct universal propositions require different \(v\)’s in their translation; else one can run into the following situation. Consider the two premises All \(x\) is \(z\) and All \(y\) is \(z\). Using the same \(v\) for their equational expressions gives \(x = vz\) and \(y = vz\), leading to the equation \(x = y\), and then to the false conclusion \(x\) equals \(y\). In chapter XV he was careful to use distinct \(v\)’s for the expressions of distinct premises. 