This is not really related to the topic but for anyone else wondering like I did for many years how this statement makes sense (given that it is usually used in a phrase meaning a single counter example proves the general case true for some inexplicable reason), the phrase actually means something else.
A single counter example can prove a general rule exists in conversation, because we don't normally isolate examples unless they're somehow special. For example, if you come to my house, and I point at one of the chairs and say "you can't sit in that chair" you would assume you could sit in one of the others even though I haven't said so.
The example on wikipedia is "parking is not allowed on Sundays", which would lead you to assume that parking was allowed on other days. As it says there, a more explicit wording would be "the exception that proves the existence of the rule."