Cutting down on all fats in your diet—no matter if they’re healthy or unhealthy—won’t make a noticeable difference in whether adults get heart disease over eight years.

The study tried lowering fat in women’s diets and also had them eat more veggies and grains, but even with less fat, their heart disease rates didn’t drop much — which supports the idea that just cutting fat, without worrying about what kind of fat or food you eat, doesn’t really help prevent heart disease.

This study looked at whether eating more or less saturated fat (like butter and cheese) affects heart problems in people who already have heart disease — and found no link. The claim is about cutting all fat, no matter what kind, and this study suggests that just cutting fat overall might not help much, since even saturated fat didn’t make things worse.

This study looked at whether eating less fat overall helps prevent heart disease, and found it doesn’t — just like the claim says. Even when people ate much less fat, their heart disease risk didn’t drop much.