Let ${\overline{L}}_{i}=(L_{i},\|\cdot\|_{i})$, $i=1,2$, be toric line bundles equipped with toric metrics and let $s_{i}$ be a toric section of $L_{i}$. By propositions 5.19 (1) and 3.38 (3)

(6.22)

$$(\psi_{{\overline{L}}_{1}\otimes{\overline{L}}_{2},s_{1}\otimes s_{2}})^{\vee}=\psi_{{\overline{L}}_{1},s_{1}}^{\vee}\boxplus\psi_{{\overline{L}}_{2},s_{2}}^{\vee}.$$

The result then follows from (6.5), the definition of the mixed integral (Definition 3.113) and Theorem 6.6. ∎