reserve n for Nat,
        lambda,lambda2,mu,mu2 for Real,
        x1,x2 for Element of REAL n,
        An,Bn,Cn for Point of TOP-REAL n,
        a for Real;
 reserve Pn,PAn,PBn for Element of REAL n,
         Ln for Element of line_of_REAL n;
reserve A,B,C for Point of TOP-REAL 2;
reserve x,y,z,y1,y2 for Element of REAL 2;
reserve L,L1,L2,L3,L4 for Element of line_of_REAL 2;
reserve D,E,F for Point of TOP-REAL 2;
reserve b,c,d,r,s for Real;

theorem Th33:
  L1 _|_ L2 implies ex x st L1 /\ L2 = {x}
  proof
    assume
A1: L1 _|_ L2;
    then
A2: L1 is being_line & L2 is being_line by EUCLIDLP:67;
A3: L1 <> L2 & L1 meets L2 by A1,EUCLIDLP:75,Th31,EUCLIDLP:109;
    not (ex x st L1 = {x} or L2 = {x}) by A2,Th7;
    hence thesis by A3,Th32;
  end;
