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 Th53:
  A\impA\andA in F
  proof
A1: A\impA\imp(A\impA\imp(A\impA\andA)) in F by Th49;
A2: A\impA in F by Th34;
    then A\impA\imp(A\impA\andA) in F by A1,Def38;
    hence thesis by A2,Def38;
  end;
