Plumbing vent question for basement bathroom

[dotom9876]

Hello: Plumbing newbie here. I am in the preliminary planning stages of adding a bathroom in my basement. So far the main unknown is venting to the "main stack". It appears that a vent does not exist for the washing machine/laundry.

What I have come across is an "Y extension tube" that is connected to the soil stack. The extension tube is about 5 - 6 inches below the main floor. Anyone know what this extension tube is for? It can't be for a basement fixture drain as it is too high. I guess it could be the drain connection extension for a another fixture from the main floor kitchen.

Is this tie in for the basement fixtures venting? Or was this previously a drain for a main floor fixture (no longer is use).

Hope I have provided enough info.

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[Cacher_Chick]

I cannot tell what the photos are showing in the overall design of the existing system.
Any vent for the basement must tie into the stack above all of the other fixture drains on the floors above, or the vent can go up and through the roof on it's own. The vent does not have to go up through the structure at the location of the new bath, it can be offset to a easier location to access, if need be.