Does the Bible really promise healing from diseases through true worship?

The bible says worship God and I will take disease away from among you, and some people think this refers to biological diseases like diabetes or cancer, but it also refers to mental diseases like anxiety or social phobia or sexual dysfunction.

And some people might wonder why religious God lovers still get disease if God promises to remove disease, and my response to that is, they might worship a highly personalized and biased image of God, instead of worshiping an unbiased and totally natural and real image of God.

Does the Bible really promise healing from diseases through true worship?
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