Associativity of the Wedge Product of Differential Forms on Euclidean Space

Let $n\in\mathbb{N}$, let $U\subseteq \mathbb{R}^n$ be open, let $k,\ell,m\in\mathbb{N}\cup\{0\}$, let $\alpha$ be a differential $k$-form on $U$, let $\beta$ be a differential $\ell$-form on $U$, and let $\gamma$ be a differential $m$-form on $U$. Then $(\alpha\wedge\beta)\wedge\gamma=\alpha\wedge(\beta\wedge\gamma).$ Consequently, whenever $\omega_1,\dots,\omega_r$ are differential forms on $U$ for some $r\in\mathbb{N}$, the expression $\omega_1\wedge\cdots\wedge\omega_r$ is unambiguous.