How to vent main floor lavatory

Can someone look at the attached diagram and tell me if the lavatory is vented properly?

The lavatory that I've drained into the cast iron stack vent resides less than 3 feet from the vent stack.

vent

It is not only not vented properly, it is not vented at all.

wet-vented?

Wouln't this be considered a wet-vent? The lavatory drain connects to the vent stack at a point higher than the toilet does, (not shown in picture, but the main floor toilet is 2 feet left of the cast iron stack), and the toilet drain enters the stack approximately 10 inches below the point where the main floor lavatory connects to the stack. how does this configuration present a siphonage problem, and thus, an improper vent situation.

As I see it, with no other fixture draining into the vent stack at a point higher than the lavatory, there is no siphonage issue. And, as I understand it, the siphonage issue is the reason for proper venting.

This is new ground for me, so please excuse my ignorance. However, I understand logic, so knowing why it isn't properly vented helps me understand the reason for the venting codes.

any thoughts?

vent

I rechecked your drawing to see if you had modified it. You show an "S" trap for the sink. That is not permitted, and an "S" trap does not have a vent so it could not be a "wet" vent for any other fixture. An "S" trap will always siphon when water runs through it.

Run the lavy waste line (1-1/2" minimum) up into the wall behind the lavy. Then extend the vent off the top of a stubout tee. The vent can either be extended thru the roof or tied into another vent somewhere between the 1st floor ceiling and the roof. Sorry, no shortcuts. Some might use an AAV. I wouldn't because they're not allowed in my area.