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

theorem
  for a,b,c being Function of Y,BOOLEAN holds a 'imp' (b '&' c) =
  (a 'imp' b) '&' (a 'imp' c)
proof
  let a,b,c be Function of Y,BOOLEAN;
    let x be Element of Y;
    ((a 'imp' b) '&' (a 'imp' c)).x =(a 'imp' b).x '&' (a 'imp' c).x by
MARGREL1:def 20
      .=('not' a.x 'or' b.x) '&' (a 'imp' c).x by BVFUNC_1:def 8
      .=('not' a.x 'or' b.x) '&' ('not' a.x 'or' c.x) by BVFUNC_1:def 8
      .='not' a.x 'or' (b.x '&' c.x) by XBOOLEAN:9
      .='not' a.x 'or' ((b '&' c).x) by MARGREL1:def 20
      .=(a 'imp' (b '&' c)).x by BVFUNC_1:def 8;
    hence thesis;
end;
