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 Th34:
  A\impA in F
  proof
A1: A\imp((A\impA)\impA)\imp(A\imp(A\impA)\imp(A\impA)) in F by Def38;
A2: A\imp((A\impA)\impA) in F by Def38;
A3: A\imp(A\impA)\imp(A\impA) in F by A1,A2,Def38;
A4: A\imp(A\impA) in F by Def38;
    thus thesis by A3,A4,Def38;
  end;
