Let $W_{2}$ be a paracompact strictly $K$-analytic space of dimension $n$ and $W_{1}\subseteq W_{2}$ a paracompact strictly $K$-analytic subdomain of $W_{2}$. Then for formally metrized line bundles $\overline{L}_{1},...,\overline{L}_{n}$ on $W_{2}$, we have $c_{1}(\overline{L}_{1})\wedge...\wedge c_{1}(\overline{L}_{n})=c_{1}\left(\overline{L}_{1}\Big|_{W_{1}}\right)\wedge...\wedge c_{1}\left(\overline{L}_{n}\Big|_{W_{1}}\right)$ in the topological interior $\overset{\circ}{W_{1}}$ of $W_{1}$ in $W_{2}$.