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 Th64:
  A\imp\not\notA in F
  proof
A1: A\imp((\notA\impA)\imp\not\notA)\imp((A\imp(\notA\impA))\imp
    (A\imp\not\notA)) in F by Def38;
A2: (\notA\impA)\imp((\notA\imp\notA)\imp\not\notA)\imp((\notA\impA)\imp
    (\notA\imp\notA)\imp(\notA\impA\imp\not\notA)) in F by Def38;
    (\notA\impA)\imp((\notA\imp\notA)\imp\not\notA) in F by Def38; then
A3: (\notA\impA)\imp(\notA\imp\notA)\imp(\notA\impA\imp\not\notA)in F
    by A2,Def38;
    (\notA\impA)\imp(\notA\imp\notA) in F by Th34,Th44; then
    \notA\impA\imp\not\notA in F by A3,Def38; then
    A\imp(\notA\impA\imp\not\notA) in F by Th44; then
A4: (A\imp(\notA\impA))\imp(A\imp\not\notA) in F by A1,Def38;
    A\imp(\notA\impA) in F by Def38;
    hence thesis by A4,Def38;
  end;
