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 Th58:
  A\impB in F iff \notB\imp\notA in F
  proof
    (\notB\imp\notA)\imp(A\impB) in F &
    A\impB\imp(\notB\imp\notA) in F by Def38,Th57;
    hence thesis by Def38;
  end;
