 Recently, the Leibniz hierarchy has been refined in Cintula &amp; Noguera 2010, 2016. The idea is to consider instead of a set of equivalence formulas \(\Delta\) (that corresponds to the biconditional) a set of formulas \([p\Rightarrow q]\) that has several properties of the usual conditional \((\rightarrow)\). Among these properties we have \((\tR_{\Rightarrow})\) and \((\tMP_{\Rightarrow})\) in the definition of protoalgebraic logic. The set \([p\Rightarrow q]\) should be such that its symetrization \([p\Rightarrow q] \cup[q\Rightarrow p]\) is a set of equivalence formulas. New classes arise when the set \([p\Rightarrow q]\) has a single element. Extensive information can be found in the recent book Cintula &amp; Noguera 2021. This book can also be taken as an introduction to abstract algebraic logic written from the perspective of the implication. 