reserve X,Y for set, x,y,z for object, i,j,n for natural number;
reserve
  n for non empty Nat,
  S for non empty non void n PC-correct PCLangSignature,
  L for language MSAlgebra over S,
  F for PC-theory of L,
  A,B,C,D for Formula of L;

theorem
  A\impB\imp\not(A\and\notB) in F
  proof
A1: A\impB\imp\notA\orB in F by Th82;
    \notA\imp\notA in F & B\imp\not\notB in F by Th64,Th34; then
    \notA\orB\imp\notA\or\not\notB in F by Th59; then
A2: A\impB\imp\notA\or\not\notB in F by A1,Th45;
    \notA\or\not\notB\imp\not(A\and\notB) in F by Th73;
    hence thesis by A2,Th45;
  end;
