reserve Y for non empty set;

theorem
  for a,b being Function of Y,BOOLEAN holds (a '&' b) 'imp' (a
  'or' b)=I_el(Y)
proof
  let a,b be Function of Y,BOOLEAN;
  for x being Element of Y holds ((a '&' b) 'imp' (a 'or' b)).x=TRUE
  proof
    let x be Element of Y;
    ((a '&' b) 'imp' (a 'or' b)).x ='not' (a '&' b).x 'or' (a 'or' b).x by
BVFUNC_1:def 8
      .=('not' a.x 'or' 'not' b.x) 'or' (a 'or' b).x by MARGREL1:def 20
      .=('not' a.x 'or' 'not' b.x) 'or' (a.x 'or' b.x) by
BVFUNC_1:def 4
      .=('not' b.x 'or' ('not' a.x 'or' a.x)) 'or' b.x
      .=('not' b.x 'or' TRUE) 'or' b.x by XBOOLEAN:102
      .=TRUE;
    hence thesis;
  end;
  hence thesis by BVFUNC_1:def 11;
end;
