Curvature of direct sum of connections equals direct sum of curvatures

Statement

Suppose $E,E'$ are vector bundles over a differential manifold $M$. Suppose $\nabla ,\nabla '$ are connections on $E,E'$ respectively. Let $R_{\nabla }$ denote the Riemann curvature tensor of $\nabla$ and $R_{\nabla }'$ denote that Riemann curvature tensor of $\nabla '$. Then if $E\oplus E'$ is the direct sum of vector bundles, $\nabla \oplus \nabla '$ is the direct sum of connections, and $R_{\nabla \oplus \nabla '}$ is its Riemann curvature tensor, we have:

$R_{\nabla \oplus \nabla '}(X,Y)(s,s')=\left(R_{\nabla }(X,Y)(s),R_{\nabla '}(X,Y)s'\right)$.