reserve Y for non empty set,
  a,b,c,d for Function of Y,BOOLEAN;

theorem Th13:
  a 'xor' a = O_el(Y)
proof
  thus a 'xor' a =('not' a '&' a) 'or' (a '&' 'not' a) by BVFUNC_4:9
    .=O_el(Y) by BVFUNC_4:5;
end;
