I will be installing a sink, shower and tiolet in a basement below an existing cleanout outlet.
I want to tie-into an existing vent pipe twenty feet away. Will this enable venting of the "gas" over this distance.

Ron

Hey Ron,
Yes! This will tie back to the DRY vent using a inverted sanitary tee. Just be sure to slope the pipe back to the group that you're venting.
If this means that you will be installing from scratch and not a preexisting rough in let me give a little advice.
Most bathroom groups are roughed in like this.
Toilet connects to sewer main or the stack vent. Lavatory connects to toilet drain and runs a vent off the top the stubout tee out the roof or revents back into a dry vent in the attic.. The toilet wet vents through the lavatory vent and the tub/shower connects to the lavatory drain and is wet vented by it. This is a normal rough in and is acceptable both by local and state codes and also The Standard Plumbing Code Book in 90 percent of the country. Check your local codes to make sure you're not in the excluded 10 percent.. The vent off the lavatory may be run out the roof or revented back into a dry vent. Good luck, Tom