reserve Y for non empty set,
  a,b,c,d for Function of Y,BOOLEAN;

theorem
  a 'imp' (b 'imp' c) = b 'imp' (a 'imp' c)
proof
  thus a 'imp' (b 'imp' c) ='not' a 'or' (b 'imp' c) by BVFUNC_4:8
    .='not' a 'or' ('not' b 'or' c) by BVFUNC_4:8
    .='not' b 'or' ('not' a 'or' c) by BVFUNC_1:8
    .='not' b 'or' (a 'imp' c) by BVFUNC_4:8
    .=b 'imp' (a 'imp' c) by BVFUNC_4:8;
end;
