Is Phyrexian Hydra a Hydra?

This question seems dumb, but [Phyrexian Hydra], as well as [Phyrexian Vatmother] and [Phyrexian Juggernaut] to name a couple others, don’t contain Phyrexian in their subtype. Instead, they have Hydra, or Horror, or Juggernaut, respectively, in their subtype.

So, are they Phyrexians? Even without it in their subtype, but in their name? I can’t find any thing about creature types being their name.