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

theorem
  ('not' a 'imp' a) 'eqv' a = I_el(Y)
proof
  ('not' a 'imp' a) 'eqv' a = (('not' a 'imp' a) 'imp' a) '&' (a 'imp' (
  'not' a 'imp' a)) by BVFUNC_4:7
    .= I_el(Y) '&' (a 'imp' ('not' a 'imp' a)) by BVFUNC_5:11
    .= (a 'imp' ('not' a 'imp' a)) by BVFUNC_1:6;
  hence thesis by Th21;
end;
