Basement Bathroom Venting Question

I am in the initial stages of beginning to finish our basement in a newly constructed home (less than 2 years old) and I have a question about extending the vent line over to the area of the 3-piece basement bathroom rough-in now to save time and money down the road with contractors.

Details prior to my questions are as follows;

As shown in the first photo (Vent Detail 1.jpg), in our main bathroom, a 1 1/2" diameter PVC vent pipe is coming down from the attic in the interior wall that is connected to a 1 1/2" diameter PVC tee. The 1 1/2" diameter PVC directly below the tee on the left side of the photo is plumbed into the basement and is connected to the 3 1/4" drain pipe from the laundry room. I assume that this is how the washing machine discharge is vented. The 1 1/2" diameter PVC on the right side of the photo also extends into the basement, but is not connected to anything and a cap was installed on the end of this pipe. The second photo (Vent Detail 2.jpg) shows the view of the 1 1/2" PVC pipes installed into the basement.

What I would like to know / confirm is if I am allowed to tie into this second 1 1/2" diameter PVC vent line that was plumbed into the basement and capped. I assume that the builder installed this vent line from above specifically for the 3-piece bathroom rough, and my plan was to extend 1 1/2" diameter PVC pipe over to the 3-piece rough, which will be located approximately 30 feet away from where the vent line plumbed into the basement is located.

I was also planning on putting a slight downward slope on this vent line to the 3-piece rough area, as when I removed the cap on the bottom of the pipe, some water drained out onto the basement floor. I question this as well, but assume the water is merely from condensation in the home’s vent system.

If anyone has any questions, or would like to see other photos to help answer my questions, please let me know.

Thank you in advance for your time and advise.

Vent Detail 1.JPG

Vent Detail 1.JPG

Vent Detail 1.JPG

Vent Detail 2.JPG

Hard to say from here…but others may be able to “see it” better than I.

I’d let a plumber handle it.

Have you considered an air admittance valve in place of all that trouble?

A future bath is what the vent was put there for.
Naturally it would have some rain water in it since it goes through the roof.

You just need to keep it pitched toward the drain as if it is a drain pipe.

Don’t worry if you make a mistake the inspector will have you tare it out and do it over.

Why not just hire a professional to do it?

Once you get your permit, your licensed plumbing contractor will be able to take care of these for you.