  We prove that if two nonzero homomorphisms from the Cuntz algebra O_infinity
to a purely infinite simple C*-algebra have the same class in KK-theory, and if
either both are unital or both are nonunital, then they are approximately
unitarily equivalent. It follows that O_infinity is classifiable in the sense
of Rordam. In particular, Rordam's classification theorem for direct limits of
matrix algebras over even Cuntz algebras extends to direct limits involving
both matrix algebras over even Cuntz algebras and corners of O_infinity for
which the K_0 group can be an arbitrary countable abelian group with no even
torsion.
