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

theorem
  a '&' (a 'nor' b) = O_el(Y)
proof
  thus a '&' (a 'nor' b) =a '&' 'not' a '&' 'not' b by Th61
    .=O_el(Y) '&' 'not' b by BVFUNC_4:5
    .=O_el(Y) by BVFUNC_1:5;
end;
