Laundry Standpipe and Venting

[Juan for the road]

I opened up a wall on the first level of my brothers 2 story,built on slab house.He wants to locate a laundry adjacent to a first floor bathroom.I located the 4" main stack(cast iron) and found an old 1 1/2" standpipe(galvanized) connected to a threaded sanitary tee about a foot off the floor.The sanitary tee outlet is a 2" that was reduced to 1 1 /2" for the standpipe.The standpipe was open and uncapped (uggh),and hidden behind a cavity wall for the plumbing.

The 4" main stack is vented straight up through the roof above the 2nd floor bath.It serves the two baths and the kitchen sink.Below the sanitary tee in the stack,the stack feeds into the building drain under the slab and out of the house,with a house trap and cleanout,then out.

I would like to install a laundry standpipe in the same location of the old one more or less.I would like to do it in 2" pvc this time.Do I need to provide additional venting? An atmospheric vent is all that would be practical if we have to.

New Jersey