Can I use only use an Air admittance valve (AAV) in a house and not have an SVP?

an aav will overcome syphonage in soil stacks but it will not prevent foul smells being pushed back through traps if you have back pressure in the system, it is always best to have an open vent on any drain or soil pipe.

As D & R Property and Plumbing Maintenance have already stated, an AAV will allow air into your waste pipes when a vacuum is formed which will prevent syphoning of traps and also prevent gurgling noises, but it doesn't allow for the build up of gasses (which occur in waste systems) to escape. You can fit an unvented "stub stack" with an AAV, but this must be connected to your waste system that is vented.

Any LABC will require the main soil stack to be vented. You can fit AAVs and anti-syphon traps to help with flow but if these fail then that’s a big problem. AAVs can fail over time, they are often hidden in walls or boxed-in so it’s against regulations to use only AAVs and have no external vent.