Let $(K,\le,\Vdash)$ be a propositional Kripke model with persistent atomic forcing and the standard forcing clauses for $\bot$, $\top$, $\land$, $\lor$, and $\to$. Let $\mathrm{IPL}$ be the natural-deduction proof system for propositional intuitionistic logic over that same formula grammar. If $\vdash_{\mathrm{IPL}} A$, then for every world $w \in K$, one has $w \Vdash A$.