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 Th67:
  A\imp\notB in F iff B\imp\notA in F
  proof
A1: A\imp\notB in F iff \not\notB\imp\notA in F by Th58;
A2: B\imp\notA in F iff \not\notA\imp\notB in F by Th58;
    B\imp\not\notB in F & A\imp\not\notA in F by Th64;
    hence thesis by A1,A2,Th45;
  end;
