venting main floor lavatory

I am adding a bathroom to my basement directly below the main floor bathroom. The main floor bathroom lavatory was setup to have a P trap, and then a two foot horizontal pipe into a 2" vent/drain pipe. That drain pipe went down through the floor, and then horizontally into the main cast iron stack. The problem is the previous owner set the horizonatl pipe below the floor, to be at a height of about five feet off the basement floor. This pipe is now in the way of my new bathroom.

I redirected the drain of this main floor lavatory to have an "S" trap, and then to go straight down through the floor, and then directly into the cast iron vent stack that it previously entered, (and at the same spot in the cast iron vent stack). So, the difference now is that the lavatory drain doesn't make the 2 foor horizontal into the vent/drain pipe.

My question is whether or not the main floor lavatory is now correctly vented. The diagram attached shows the new drain layout. The main floor lavatory is less than 3 feet measured horizontally, from the main cast iron stack.

S-trap are illegal under all codes.

You can't do it like that.

You need to vent it before the tie in or unless the stack is with-in 3'6" then you can use the stack for the vent.

See how tub connects to the vent, same way with the lav and you will be set.