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David Foster just put all the doubters to rest ... saying Yolanda Foster﻿'s battle with Lyme disease is very real and very serious.

In a statement obtained by TMZ ... Foster backs his ex, saying, "it is so frustrating to see headlines questioning her chronic debilitating illness." Foster's addressing several reports that have suggested Yolanda might not actually be as sick as she claims.

Foster gives Yolanda even more props ... saying he's proud of Yolanda's fight and how brave and open she's been in finding a cure for the disease.

It makes sense ... TMZ broke the story -- David's been the one to foot all of Yolanda's medical bills -- even after their split, so you gotta assume he knows what's going on with her health.