  In LT, prior to chapter XV, the one on Aristotelian logic, Boole’s examples only used universal propositions. (One can speculate that he had encountered difficulties with particular propositions and avoided them.) Those of the form All x is y were first expressed as \(x = vy\), and then \(v\) was promptly eliminated, giving \(x = xy\). (Similarly if \(x\) was replaced by not-\(x\), etc.) Boole said the elimination of \(v\) was a convenient but unnecessary step. For the examples of  All x is y in the first fourteen chapters he could simply have used the expression \(x = xy\), skipping the use of the parameter \(v\). 