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 Th102:
  A\impB in F implies C\impA\imp(C\impB) in F
  proof
    C\impA\imp(A\impB\imp(C\impB)) in F by Th39;
    then A\impB\imp(C\impA\imp(C\impB)) in F by Th38;
    hence thesis by Def38;
  end;
