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

theorem Th4:
  a 'imp' b = a 'imp' (a '&' b)
proof
  a 'imp' (a '&' b)='not' a 'or' (a '&' b) by BVFUNC_4:8
    .=('not' a 'or' a) '&' ('not' a 'or' b) by BVFUNC_1:11
    .=I_el(Y) '&' ('not' a 'or' b) by BVFUNC_4:6
    .='not' a 'or' b by BVFUNC_1:6;
  hence thesis by BVFUNC_4:8;
end;
