 The first concerns the deduction theorem. To prove a general theorem relating the existence of a deduction theorem with an algebraic property requires first that a concept of deduction theorem applicable to any logic has to be defined. A logic \(\bL\) has the deduction-detachment property if there is a finite set of formulas \(\Sigma(p, q)\) such that for every set of formulas \(\Gamma\) and all formulas \(\phi , \psi\)