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 Th71:
  \not(A\orB)\imp\notA\and\notB in F
  proof
    A\impA\orB in F & B\impA\orB in F by Def38; then
A1: \not(A\orB)\imp\notA in F & \not(A\orB)\imp\notB in F by Th58;
    \not(A\orB)\imp\notA\imp(\not(A\orB)\imp\notB\imp(\not(A\orB)\imp\notA\and
    \notB)) in F by Th49; then
    \not(A\orB)\imp\notB\imp(\not(A\orB)\imp\notA\and\notB) in F by A1,Def38;
    hence thesis by A1,Def38;
  end;
