reserve n for Nat;
reserve i for Integer;
reserve r,s,t for Real;
reserve An,Bn,Cn,Dn for Point of TOP-REAL n;
reserve L1,L2 for Element of line_of_REAL n;
reserve A,B,C for Point of TOP-REAL 2;

theorem Th7:
  An in Line(Bn,Cn) & An <> Cn implies Line(Bn,Cn) = Line(An,Cn)
  proof
    assume that
A1: An in Line(Bn,Cn) and
A2: An <> Cn;
    Cn in Line(Bn,Cn) & An in Line(Bn,Cn) by A1,EUCLID_4:41;
    hence thesis by A2,EUCLID_4:43,EUCLID_4:42;
  end;
