I want to add a sink drain from and adjacent room to an existing laundry room. The original drain design does not physically allow space for another connection to the stack below the existing washer drain (see original below). I am thinking of modifying the washer P-trap and using the existing drain connection for the new sink drain (see proposed). Is the wet stack arrangement acceptable or do I need a vent on the sink drain?

Original:

Proposed:

Photo of original:

Thanks for any help... Kurt