 The language we consider is the set \(\{\wedge , \vee , \rightarrow , \neg \}\), where \(\wedge , \vee , \rightarrow\) are binary connectives and \(\neg\) a unary connective. A Hilbert style axiomatization for \(\bR\) can be given by the rules of Intuitionistic Linear Logic without exponentials and the axioms L2, L3, L7-L12 of this logic together with the axioms