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
  A\imp(B\imp(A\impB)) in F
  proof
    (B\imp(A\impB))\imp(A\imp(B\imp(A\impB))) in F &
    (B\imp(A\impB)) in F by Def38;
    hence thesis by Def38;
  end;
