The language of modal logic we consider here is the set \(L_m = \{\wedge , \vee , \rightarrow , \neg , \Box , \top , \bot \}\) that expands \(L_c\) by adding the unary connective \(\Box\). In the standard literature on modal logic a normal modal logic is defined not as a consequence relation but as a set of formulas with certain properties. A normal modal logic is a set \(\Lambda\) of formulas of \(L_m\) that contains all the tautologies of the language of classical logic, the formulas of the form \[\Box(\phi \rightarrow \psi) \rightarrow(\Box \phi \rightarrow \Box \psi)\] and is closed under the rules