Lemma 15.90.9. Let $A$ be a ring. Let $f, g \in A$. Then for $K \in D(A)$ we have $R\mathop{\mathrm{Hom}}\nolimits _ A(A_ f, R\mathop{\mathrm{Hom}}\nolimits _ A(A_ g, K)) = R\mathop{\mathrm{Hom}}\nolimits _ A(A_{fg}, K)$.

**Proof.**
This follows from Lemma 15.72.1.
$\square$

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