reserve Y for non empty set;

theorem
  for a,b being Function of Y,BOOLEAN holds 'not'( a 'or' b) 'imp'
  'not' a=I_el(Y)
proof
  let a,b be Function of Y,BOOLEAN;
  for x being Element of Y holds ('not'( a 'or' b) 'imp' 'not' a).x=TRUE
  proof
    let x be Element of Y;
    ('not'( a 'or' b) 'imp' 'not' a).x ='not' ('not'( a 'or' b)).x 'or' (
    'not' a).x by BVFUNC_1:def 8
      .='not' 'not' (a 'or' b).x 'or' ('not' a).x by MARGREL1:def 19
      .=(a 'or' b).x 'or' 'not' a.x by MARGREL1:def 19
      .=(a.x 'or' b.x) 'or' 'not' a.x by BVFUNC_1:def 4
      .=(a.x 'or' 'not' a.x) 'or' b.x
      .=TRUE 'or' b.x by XBOOLEAN:102
      .=TRUE;
    hence thesis;
  end;
  hence thesis by BVFUNC_1:def 11;
end;
