reserve A for set;
reserve X,Y,Z for set,x,x1,x2,y,y1,y2,z,z1,z2 for object;
reserve u for UnOp of A,
  o,o9 for BinOp of A,
  a,b,c,e,e1,e2 for Element of A;

theorem Th9:
  e1 is_a_left_unity_wrt o & e2 is_a_right_unity_wrt o implies e1 = e2
proof
  assume that
A1: e1 is_a_left_unity_wrt o and
A2: e2 is_a_right_unity_wrt o;
  thus e1 = o.(e1,e2) by A2
    .= e2 by A1;
end;
