How to add standpipe in in basement?

Hello, first post on here. I'm looking for some advice.

I need to add a standpipe in my basement for my water softener and furnace/AC condensate pump drain. I am told this should be a 2" standpipe.

I will be adding this standpipe right at the location shown in the first photo. The larger pipe is 3" copper coming from the bathroom right above the smaller pipe to the right is 2" copper and I believe it is a vent for the basement bathroom on the other side of the wall you see. The bathroom sink drains into this 2" line about 18" above the basement floor, above that point no other fixtures drain into this pipe and it is only a vent going up.

Can I tie my standpipe into this 2" line? If so should it tie in above or below the basement sink drain? Do I use a wye or a tee fitting to tie into the vertical line? I plan on cutting the copper and using 2 transition fernco couplings between the copper and abs.

Thanks very much.
John

If the sink or lav is 2", then you can cut in a santee below the sink trap arm, and add a 2" trap there.
Most places will want to see that trap arm vented, and then revented back to the sink vent at 42" or move above the floor.

The same thing can also be done with the 3", as long as it's vented before entering the stack.

Thanks very much.

John