Bath lav vent and drain question

Is it acceptable to run a 2 foot T from a vent pipe to my single bathroom sink drain? I have a 1 1/2" vent pipe in the wall about 2 feet from my sink. I have double wall below the countertop but single wall above it so I can't run any venting above sink. The vertical vent pipe is in a double wall in the shower next to the sink. I would like to just run a sloped ABS section from the vertical vent to the middle of the area below sink and attach my sink p trap there. What do you think? Thanks.

What makes you say it is a vent pipe and not a drain?
What is it venting?

Good question. Right now what I have is a gutted bathroom with stud walls. I called it a vent since it goes through the roof and is cut off about half way down the wall. It was the vent for the old shower drain which is being relocated. The shower drain and sink drain will be new and splice into existing waste line. Now I want to tie into this 1 1/2" ABS (vent) and continue it down to underneath the house and then tie into the waste line. Just not sure if a 2 foot extension from the vent/drain line is appropriate pumping procedure. I hope this makes sense.

Okay, A 2' dirty arm into a sani-tee is probably okay there but there is a little doubt in my mind that it was just venting the shower. Is everything you have now vented properly? Or, will taking this off the present line be removing a wet vent from something like a toilet?

Once water goes in a pipe it becomes a drain. While it is possible to wet vent using that drain it is not allowed to wet vent between floors. If this is used as a vent at a lower level it must come off the vent at least 6" above the flood rim of the kitchen sink you are installing to be a useable vent below.

drain

The way you SAY it is correct. However, you could still DO it wrong, so a picture or drawing of exactly HOW you want to do it would be more precise.