I am looking for a *reference* for the following basic fact:

Let $R$ be a noetherian ring, let $M$ be an artinian $R$-module, let $N$ be a finitely generated $R$-module, and let $i\in\mathbb{N}$. Then, $Tor_i^R(M,N)$ is artinian.

(I know that it is easy to prove. I guess nevertheless that this is written down somewhere in the standard literature about homological algebra, and I would like to know where.)

*Remark 1:* The above conclusion also holds if $R$ is coherent, $M$ is artinian, and $N$ is of finite presentation. A reference for this generalisation would also be fine.

*Remark 2:* Leamer proves in his PhD Thesis (2010) a generalisation to the case where $R$ is noetherian, $M$ is artinian, and $N$ is minimax. But I guess there must be an earlier reference for the less general case.