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\or(B\orC)\imp(A\orB)\orC in F
  proof
A1: A\imp(A\orB)\orC\imp(B\orC\imp(A\orB)\orC\imp(A\or(B\orC)\imp(A\orB)\orC))
    in F by Def38;
    A\impA\orB in F & A\orB\imp(A\orB)\orC in F by Def38; then
    A\imp(A\orB)\orC in F by Th45; then
A2: B\orC\imp(A\orB)\orC\imp(A\or(B\orC)\imp(A\orB)\orC) in F by A1,Def38;
    B\impA\orB in F & C\impC in F by Def38,Th34; then
    B\orC\imp(A\orB)\orC in F by Th59;
    hence thesis by A2,Def38;
  end;
