Basement Bathroom - Need Waste/Vent Help

Hello everyone. I am planning on installing a bathroom in my basement. The 4 inch cast iron sanitary drain for the house runs beneath the slab (essentially right next to the bathroom location). I plan on chopping up the concrete in order to tap into the line. I have some concerns about proper venting. The bathroom will consist of a toilet, shower and sink. I know venting isn't required if the fixture is connected to the vertical stack within a certain distance, but I am not sure about tapping a horizontal.

After the new proposed bath, the existing horizontal sanitary line continues to a fresh air inlet, then a house trap, then off to the cesspool.

The existing vertical stack is not close enough to use.

Thanks for any help.

venting

You may know just enough about plumbing to be dangerous. It makes NO difference how close you are, or whether you attach directly, to a vertical pipe. The pipe may already be a vent which means you cannot use it for a drain, OR it might be a drain line, in which case it cannot be "converted" to a vent. You have to provide proper vents and connect them to existing vents or run them out through the roof.

Helpful Plumbing Hints for Residential Construction by Bert Polk Plumbing Inspector Lincoln County

Thanks anyway.