Weak exceptional zero conjecture for Rubin–Stark elements

Let $\Lambda=\mathcal{O}_p[[\Gamma]]$, let $(U_\infty')^\chi$ be the $\chi$-component of the inverse limit of the $p$-unit modules, let $\varepsilon_\infty^\chi$ be the inverse-limit Rubin–Stark element, and let $\mathcal{A}$ be the augmentation ideal of $\Lambda$. Weak exceptional zero conjecture for $\chi$.

$$\varepsilon_\infty^\chi\in\mathcal{A}^{f}\cdot\bigwedge^{d^+}(U_\infty')^\chi.$$

The source states that this follows from the corresponding Iwasawa main conjecture and identifies it with an exceptional zero conjecture for Rubin–Stark elements in related work. No independent resolution is supplied.