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 'nor' (a 'nand' b) = O_el(Y)
proof
  thus a 'nor' (a 'nand' b) = 'not' a '&' a '&' b by Th37
    .= O_el(Y) '&' b by BVFUNC_4:5
    .= O_el(Y) by BVFUNC_1:5;
end;
