Basement bathroom venting question

Hi experts,

I am in the process of finishing my basement which includes a bathroom. The basement was roughed in for a bathroom when we bought the house, and this is the current setup. There are two stubs sticking out of the concrete. One is 2" while the other is 3" (I am assuming that the smaller pipe is for the faucet drain and the big one is for the WC). There is also a gravel hole in the vicinity, which I assume is for a shower or bathtub. There is a sewage pump adjacent to the bathroom area (in addition to a sump pump) and both the pipes drain into the sewage pump which ejects everything out of the house through a 3" pipe (I confirmed this by pouring water down both pipes). The sewage pump is vented, and the 2" vent pipe from the sewage pump connects to a 2" pipe coming out of the concrete and going up to the first floor (possibly to the vent stack?) 20 feet away.

I would like to add a wet bar around 35 feet away from the faucet drain. I can get a drain line from the wet bar to the faucet drain with 1/8" slope/foot. My question is, what would be the best way to vent the whole setup? Would I need a separate vent from the bar faucet and the bathroom faucet? Or would a single vent from the drain faucet be sufficient? Would it be OK to connect the vent from the faucet(s) to the sump pump vent, or would I need to take it all the way to the pipe to which the sewage pump connects?

Apologize for some of the layman terms, since I am completely new to plumbing. Any help would be extremely appreciated.

you have to go 1/4 ipf for 1-1/2 and 2" drainage pipe.
You can vent into the existing 2"

Wally Hays said:

you have to go 1/4 ipf for 1-1/2 and 2" drainage pipe.
You can vent into the existing 2"

Click to expand...

Thanks for your reply. I think I should be able to get 1/4 ipf for the drain. Does it make a difference if there was only one vent ( a T from the faucet drain and bar drain) venting to the sump pump vent than going to the other one?