If other life exists there is no reason to assume that it
came to technical competence at exactly the same time as
we did. In fact, given the lifetime of the universe, it
would have likely gotten its space legs long ago.
If they could, they would have built self replicating
machines to explore space. These machines would have very
quickly (in galatic terms) become ubiquitous in the galaxy
(i don't remember if he generalized to the universe or not)
and we would have observed them by now. Since we don't we
must be alone.
I apologize for the poor quality of the above quote, but i
think it more or less conveys von Neumanns argument. Note
that it has a number of assumptions in it... (i have no
intentions of defending the above 'proof').