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When Danny says I swear to Google he's basically saying he's checked every single fact and if you don't believe him he'll make you look it up and you'll probably regret it.
Danny: I swear to Google, that movie came out in 1999. You: No way. Danny: Look it up.
Danny: I swear to Google, that's not how it works. You: It is. Danny: Prove it.
Danny: I swear to Google, I didn't eat the last slice. You: You did. Danny: Google says otherwise.