The existence of mild solutions is proven for the first-order delay semilinear evolution inclusion with nonlocal condition \[ y'-A(t)y \in F \biggl(t,y \bigl(\sigma(t) \bigr)\biggr),\;t\in J=[0,b], \quad y(0)+ f(y)=y_0, \] in a real Banach space \(E\). \(A(t)\) is the infinitesimal generator of a linear semigroup; \(F:J\times E\to 2^E\) is strongly measurable in \(t\), upper semicontinuous in \(y\) and bounded-closed-convex-valued; \(\sigma:J\to J\) is continuous and satisfies \(\sigma(t)\leq t\) for all \(t\in J\); \(f:C(J,E)\to E\) is continuous and bounded; and \(y_0\in E\). The result is proven by applying a fixed-point theorem due to M. Martelli [Boll. Unione Mat. Ital. (4), 11, Suppl. Fasc., No. 3, 70-76 (1975; Zbl 0314.47035)].