Honey Boo Boo 's dad is doing just fine, TMZ has learned ... following rumors he died in a tragic car accident.

And, we even have video to prove it! Check it out -- Mike Thompson says in the clip recorded Saturday he's "alive and well" ... just living life "day by day" in Georgia. Phew! Getty

You may have seen ... there were some unsubstantiated social media rumors that he had passed away earlier this week. Honey Boo Boo -- real name Alana Thompson -- didn't feed into the chatter.

Mike shares Alana with June "Mama June" Shannon . They split in 2014 and don't have a relationship at this point. He is also estranged from Alana. Gallery Launch Gallery

Earlier this year, the former "Toddlers and Tiaras" star reflected on a 2014 car crash they were involved in, debating to

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