Bathroom venting

Hello Everyone,
First time user and requesting some help on a bathroom remodel wrt to proper venting. I attached a photo showing a small bathroom. I'm replacing a tub with a shower unit and relocating a LAV from the left wall to the bottom wall. Replaced the existing 1 1/2" pvc/ original galv. pipe with new 2" pvc. Followed the sames basic route due to major notching in the joists. Because I have elevation issues between the joists (2x8s) couldn't figure how to dry vent the shower without raising the subfloor a few inches. Was hoping I could use the LAV drain as a wet vent for the shower. The distance from the shower trap to the lav vent is less than 8 feet. Toilet has a 3" drain and was converted to PVC as part of a previous remodel. Virginia construction circa 1936.
Any help would be appreciated.
Thanks!

Vent

Don't know about Va. but AL code allows you to vent what I see (shower and Lav). The only question "is the toilet vented seperately"? Did not see it!

Thanks very much. I'll be looking in the cavity where the 3" toilet drain is - should be a vent downstream of this bath as a plumber installed another bath group adjacent to this bath as part of a separate remodel. He had replaced the existing 3" cast iron piping when this was done.
Thanks again and I'll let you know what I find.

OK, finally got to opening up the cavity. There's a 2" vent 4-6" downstream of the closet flange. It goes straight up to the attic and through the roof. There looks to be another vent pipe (from the adjacent bathroom group) that must tee into this pipe somewhere in the wall (don't see it in the attic).
Think venting for this toilet should be good to go then, right?