Hello. Building a powder bath in a second floor loft. Ceiling is a vault. So I the issue is where adding a second bath/(lav and toilet) . We have room to get the 3” down to crawlspace and tie in. The 3” would run a max distance of 4’ horizontal in the joist bay until it will drop into a vertical 3” to crawlspace. The lav will run into a 3x2 wye placed below joist level vertical in the stack heading down to crawlspace. The original plumbing has an 1-1/2” vent horizontal running through one of the joist bays that would be above the 2” lav pipe horizontally. The vent termination on the roof is approximately 5 feet above second floor level. My question is am I able to tie into the 1-1/2” vent with a tee into the 2” lav pipe for vent purposes?