One-dimensional Noetherian domain implies Cohen-Macaulay

This article gives the statement and possibly, proof, of an implication relation between two commutative unital ring properties. That is, it states that every commutative unital ring satisfying the first commutative unital ring property must also satisfy the second commutative unital ring property
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Statement

Property-theoretic statement

The property of commutative unital rings of being a one-dimensional Noetherian domain is stronger than the property of being a Cohen-Macaulay ring.

Verbal statement

Any one-dimensional domain (i.e. a Noetherian domain whose Krull dimension is exactly one) is Cohen-Macaulay.