It featured on a few Tom & Jerry cartoons, usually after something (e.g. that radioactive white mouse) had blown up the entire earth or something. Tom would say, in a booming, doom-laden voice: “Dooooon’t you belieeeeeve it”.
A poster on this forum suggests that it may have been something to do with a Ripley’s Believe It Or Not film from the 1930’s. Can anyone here corroborate or refute that?