Because the anonymous hash is built with keys as the values of the original hash and values as the keys of the original hash, and identical later keys supercede earlier keys, it will have only one key for each unique value from the original hash. So if it ends up with 1 key all the values of the original hash were equal (and if it ends up with 0 keys, the original hash was empty, which may or may not count as having all values equal).