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 'nand' 'not' a = I_el(Y) & 'not' (a 'nand' 'not' a) = O_el(Y)
proof
  a 'nand' 'not' a = 'not' (a '&' 'not' a) by th1
    .= 'not' O_el(Y) by BVFUNC_4:5
    .= I_el(Y) by BVFUNC_1:2;
  hence thesis by BVFUNC_1:2;
end;
