Hello. We’re adding a second floor powder bath. It has a vaulted ceiling/steep pitch roof. So the plan is to run a 3” pipe horizontally to catch the toilet approximately 4 ‘ between the joist bay and drop it down vertically in a wall space to the crawlspace below. On the vertical 3” pipe will be a 3x2 wye to catch lav drain running below floor joists. Reason being there is space approximately 3” above a false ceiling where we can run this pipe. But in an adjacent joist bay there is a 1-1/2 vent running horizontally that will intersect above this 2” lav waste that runs across to catch another lower floor bath and then exits out the roof. The vent termination is 4-5’ above the the second floor level. Can I tie the 2” lav into the 1-1/2 with a tee at the intersection and use that as a vent for powder bath? The 2” will be horizontal below floor joists and the 3” horizontal pipe for toilet is above that in the joist bay remember. Thank you in advance.