As pointed out by Derek Barton, this mechanism can only occur in cyclohexane if two particular atoms are trans diaxial.  
A major piece of evidence in support of this mechanism is the deuterium isotope effect, whereby one example of this kind of reaction occurs seven times slower with a deuterium bromide involved compared with a hydrogen bromide.  As pointed out by Derek Barton, this mechanism can only occur in cyclohexane if two particular atoms are trans diaxial.  It occurs with anti periplanar geometry because that allows for the greatest overlap as sigma orbitals become pi orbitals in the new compound, the formation of which is governed by Zaitsev's rule.  FTP name this mechanism in which a strong base reacts with an alkyl halide in a single step to remove a hydrogen and the halogen opposite it, resulting in a carbon-carbon double bond.
A major piece of evidence in support of this mechanism is the deuterium isotope effect, whereby one example of this kind of reaction occurs seven times slower with a deuterium bromide involved compared with a hydrogen bromide.  
E2 [accept bimolecular elimination (either order)]