In this paper we study the algebras obtained by having the deduction theorem on the sets of two elements, calling them Q.H.-algebras .Adding to them the FREGE'S law, we obtain a Hilbert algebra ; adding to them the law (x .y) .y = (y .x) .x, we obtain that thay form a variety; suposing the existence of a least element to the later , we obtain an ortolattice wich gives a boolean algebra on an ortomodular lattice, according to the nature of implication classical or strong.