Vent Question for bar sink

Where does a vent for a sink need to be? We have a basement bar sink that will be tied back to the main drain 7 feet away. At the tie in point to the main drain is the vent stack shared by the bathroom. See picture below. I am just wondering if the current vent stack is enough for venting the bar sink or does it need a separate vent?

The bar sink also needs a vent.
Venting the lav does nothing for the bar sink.

Helpful Plumbing Hints for Residential Construction by Bert Polk Plumbing Inspector Lincoln County

The vent is above the trap arm for the bar sink.