reserve Y for non empty set;
reserve Y for non empty set;

theorem
  for a being Function of Y,BOOLEAN holds a 'imp' I_el(Y) = I_el(Y )
proof
  let a be Function of Y,BOOLEAN;
  for x being Element of Y holds (a 'imp' I_el(Y)).x = TRUE
  proof
    let x be Element of Y;
    (a 'imp' I_el(Y)).x ='not' a.x 'or' (I_el(Y)).x by BVFUNC_1:def 8
      .='not' a.x 'or' TRUE by BVFUNC_1:def 11;
    hence thesis;
  end;
  hence thesis by BVFUNC_1:def 11;
end;
