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

theorem
  for a,b,c,d being Function of Y,BOOLEAN holds (a 'or' b 'or' c)
  'imp' d = (a 'imp' d) '&' (b 'imp' d) '&' (c 'imp' d)
proof
  let a,b,c,d be Function of Y,BOOLEAN;
    let x be Element of Y;
    ((a 'imp' d) '&' (b 'imp' d) '&' (c 'imp' d)).x =((a 'imp' d) '&' (b
    'imp' d)).x '&' (c 'imp' d).x by MARGREL1:def 20
      .=(a 'imp' d).x '&' (b 'imp' d).x '&' (c 'imp' d).x by MARGREL1:def 20
      .=('not' a.x 'or' (d).x) '&' (b 'imp' d).x '&' (c 'imp' d).x by
BVFUNC_1:def 8
      .=('not' a.x 'or' (d).x) '&' ('not' b.x 'or' (d).x) '&' (c 'imp' d
    ).x by BVFUNC_1:def 8
      .=((d).x 'or' 'not' a.x) '&' ('not' b.x 'or' (d).x) '&' ('not' (c)
    .x 'or' (d).x) by BVFUNC_1:def 8
      .=('not'( a.x 'or' b.x) 'or' (d).x) '&' ('not' c.x 'or' (d).x)
    by XBOOLEAN:9
      .=((d).x 'or' 'not' (a 'or' b).x) '&' ('not' c.x 'or' (d).x) by
BVFUNC_1:def 4
      .=('not'( (a 'or' b).x 'or' c.x)) 'or' (d).x by XBOOLEAN:9
      .='not' (a 'or' b 'or' c).x 'or' (d).x by BVFUNC_1:def 4
      .=((a 'or' b 'or' c) 'imp' d).x by BVFUNC_1:def 8;
    hence thesis;
end;
