Bell's theorem without inequalities and without probabilities for two observers

A proof of Bell's theorem using two maximally entangled states of two qubits is presented. It exhibits a similar logical structure to Hardy's argument of nonlocality without inequalities. However, it works for 100% of the runs of a certain experiment. Therefore, it can also be viewed as a Greenbrrger-Horne-Zellinger-like proof involving only two spacelike separated regions.