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Taylor Swift & Travis Kelce 's "Love Story" wasn't the main focus of a recent event ... 'cause a different couple was getting married, and they just looked on!

The A-list couple was spotted in Tennessee at a backyard wedding ... definitely drawing eyes off the bride and groom, though we're sure they didn't mind. TMZ.com

Taylor's dressed in an ankle-length blue dress while Travis is decked out in slacks and a button-down shirt ... and, though they're two of the biggest stars in the country, they're chatting with everyone like they're any other couple.

The two are smiling and laughing a lot ... though there's no PDA in the snaps -- so, looks like they're on their best behavior around everyone else.

Photos are spreading like wildfire online ... and, it looks like some

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