No, it isn’t false at all. The vaccine absolutely reduces your chance of getting Covid to begin with, even the delta variant. If you have a much smaller chance of getting it, means there is a much smaller percentage of the population who has it to spread in the first place. So yes, it does slow the spread. And even if you catch it while vaccinated, if everyone around you is vaccinated it reduces the likelihood of them catching it from you. This isn’t fucking complicated.
Okay cool, way to restate your straw man, you’re literally ignoring that the entire point that the claim that vaccinated people don’t spread the virus as much as vaccinated people has been debunked.