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

theorem
  (a 'imp' b) '&' (a '&' c) 'imp' (b '&' c) = I_el(Y)
proof
  (a 'imp' b) '&' (a '&' c) 'imp' (b '&' c) =((a 'imp' b) '&' a) '&' c
  'imp' (b '&' c) by BVFUNC_1:4
    .=(a '&' b) '&' c 'imp' (b '&' c) by BVFUNC_6:56
    .=a '&' (b '&' c) 'imp' (b '&' c) by BVFUNC_1:4;
  hence thesis by BVFUNC_6:38;
end;
