Adding a 1/2 bath in basement - this rough in look ok?

New on the forum here but have lurked a long time. Great info from a lot of knowledgeable people. Thanks.

Just wanted a look at a pretty basic 1/2 bath addition in a basement in upstate NY.

Tapped into existing 3" drain line under slab. About 2-3' to the right is the main vertical stack coming down from above floors. On the wall to the right is an existing mud-sink with its own vent.

I understand that because I am within 6' of the stack the toilet will not need its own vent.
This look ok?

The toilets from above will affect the lower toilet if it's not vented.

You need a vent between the toilet and the waste stack or waste horizontal.

Thanks Terry
"will affect" meaning it wont work or something more subtle? This is the case even with 3" lines and the vertical stack less than 3' away from this new wye? Have been told that close it wouldn't need its own vent.

Look at it this way- the stack is not and cannot be used as a vent if there is any drainage coming into it from above.
It does not matter what size or how far away it is.

quote; Have been told that close it wouldn't need its own vent.

Who told you this? Someone from Home Depot?