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

theorem
  for a being Function of Y,BOOLEAN holds a 'imp' O_el(Y) = 'not' a
proof
  let a be Function of Y,BOOLEAN;
    let x be Element of Y;
    (a 'imp' O_el(Y)).x ='not' a.x 'or' (O_el(Y)).x by BVFUNC_1:def 8
      .='not' a.x 'or' FALSE by BVFUNC_1:def 10
      .='not' a.x;
    hence thesis by MARGREL1:def 19;
end;
