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
  \not(A\and\notA) in F
  proof
    \notA\imp\notA in F & A\imp\not\notA in F by Th34,Th64; then
    \notA\andA\imp\notA\and\not\notA in F &
    \notA\and\not\notA\imp\not(A\or\notA) in F by Th74,Th72; then
    \notA\andA\imp\not(A\or\notA) in F by Th45; then
    \not\not(A\or\notA)\imp\not(\notA\andA) in F &
    A\or\notA\imp\not\not(A\or\notA) in F by Th64,Th58; then
    (A\or\notA)\imp\not(\notA\andA) in F & A\or\notA in F by Th45,Def38; then
A1: \not(\notA\andA) in F by Def38;
    A\and\notA\imp\notA\andA in F by Th50; then
    \not(\notA\andA)\imp\not(A\and\notA) in F by Th58;
    hence thesis by Def38,A1;
  end;
