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 Greenberger-Horne-Zeilinger-like proof involving only two spacelike separated regions.