reserve AS for AffinSpace;
reserve A,K,M,X,Y,Z,X9,Y9 for Subset of AS;
reserve zz for Element of AS;
reserve x,y for set;

theorem Th3:
  AS is AffinPlane & X is being_plane & Y is being_plane implies X= Y
proof
  assume that
A1: AS is AffinPlane and
A2: X is being_plane and
A3: Y is being_plane;
  X=the carrier of AS by A1,A2,Th2;
  hence thesis by A1,A3,Th2;
end;
