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

theorem
  for a being Function of Y,BOOLEAN holds O_el(Y) 'imp' a = I_el(Y )
proof
  let a be Function of Y,BOOLEAN;
  for x being Element of Y holds (O_el(Y) 'imp' a).x = TRUE
  proof
    let x be Element of Y;
    (O_el(Y) 'imp' a).x ='not' (O_el(Y)).x 'or' a.x by BVFUNC_1:def 8
      .=TRUE 'or' a.x by BVFUNC_1:def 10;
    hence thesis;
  end;
  hence thesis by BVFUNC_1:def 11;
end;
