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QUICK ANSWER
"There is not" is a phrase which is often translated as "no hay", and "there is no" is a phrase which is also often translated as "no hay". Learn more about the difference between "there is not" and "there is no" below.
there is not(
thehr
ihz
nat
)A phrase is a group of words commonly used together (e.g., once upon a time).
a. no hay
There is not a doubt in my mind that Manuel is guilty of fraud.No hay duda en mi mente que Manuel es culpable de fraude.