Plumbing for 60” double vanity vent needed?

[Hioutput1]

So I’m in the middle of re-plumbing this house I just bought. Researched lots of info on here but cant find definitive answer to my question. It was originally plumbed with single vanity and want to install a double vanity, my question is do I need a vent at the tee for the for the vanity or is it fine the way I have it in the pic since it drains out to the 4” vertical vent that has nothing draining down from above? I can’t tie into the 4” stack so I would have to go straight up through roof or use AAV. Thanks for any advice. IPC code in RI

 

[GReynolds929]

In my area none of that is vented properly.

 

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[Hioutput1]

This is how it was setup originally in cast iron and copper, I just replicated what was there in pvc to make sure that that part of it would work as it was working before. Only difference here is it was a single vanity.