Pass. side hoses to radiator (transmission or not)?

[Subix]

As the title suggests, is this one of the the hoses from the transmission into the radiator to cool it? For the life of me I've spent 40 minutes trying to find a diagram that shows it but I fail. Apparently I also have all the PDF service manual sections except the transmission? Nice.

From what I can see on Subaruparts it appears to actually be the driver side. However, if that is the case... what hose is this too? If it IS the transmission cooling line, that would quite possibly explain the billion air bubbles in the ATF. If it's not then wth is it? (is the power steering cooled somehow through the rad too?)