We propose no-hidden-variable theorem for the quantum measurement outcomes by measuring an observable that is obtained through a single projection operator. We are in the inconsistency within hidden-variable theories when the first predetermined hidden result is $+1$ by measuring a single projection operator $|uparrowanglelangleuparrow|$ in the quantum state $|uparrowangle$, the second predetermined hidden result is the same $+1$ asby measuring the same projection operator $|uparrowanglelangleuparrow|$ in the same quantum state $|uparrowangle$, and then we consider the existence of only the following proposition $[|uparrowanglelangleuparrow|,|uparrowanglelangleuparrow|] = 0$and we assign the value ``1'' for the commutator. It turns out that we cannot assign the predetermined hidden result for quantum measurement outcome as $+1$ when measuring a single projection operator. Based on the argumentations, we propose an experimental accessible hidden-variable inconsistency in terms of the imperfect source and detector.