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

theorem
  a 'or' b = (a 'imp' b) 'imp' b
proof
  thus (a 'imp' b) 'imp' b ='not' (a 'imp' b) 'or' b by BVFUNC_4:8
    .='not' ('not' a 'or' b) 'or' b by BVFUNC_4:8
    .=('not' 'not' a '&' 'not' b) 'or' b by BVFUNC_1:13
    .=(a 'or' b) '&' ('not' b 'or' b) by BVFUNC_1:11
    .=(a 'or' b) '&' I_el(Y) by BVFUNC_4:6
    .= a 'or' b by BVFUNC_1:6;
end;
