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 Th70:
  \not(A\andB)\imp\notA\or\notB in F
  proof
    \notA\imp\notA\or\notB in F & \notB\imp\notA\or\notB in F by Def38; then
    \not(\notA\or\notB)\imp\not\notA in F & \not\notA\impA in F &
    \not(\notA\or\notB)\imp\not\notB in F & \not\notB\impB in F
    by Th58,Th65; then
A1: \not(\notA\or\notB)\impA in F & \not(\notA\or\notB)\impB in F by Th45;
    \not(\notA\or\notB)\impA\imp(\not(\notA\or\notB)\impB\imp
    (\not(\notA\or\notB)\impA\andB)) in F by Th49; then
    \not(\notA\or\notB)\impB\imp(\not(\notA\or\notB)\impA\andB) in F
    by A1,Def38; then
    \not(\notA\or\notB)\impA\andB in F by A1,Def38; then
    \not(A\andB)\imp\not\not(\notA\or\notB) in F &
    \not\not(\notA\or\notB)\imp(\notA\or\notB) in F by Th58,Th65;
    hence thesis by Th45;
  end;
