  We present a parity-doublet theorem for the representation of the intrinsic
parity of Majorana fermions, which is expected to be useful also in condensed
matter physics, and it is illustrated to provide a criterion of
neutron-antineutron oscillation in a BCS-like effective theory with $\Delta
B=2$ baryon number violating terms. The CP violation in the present effective
theory causes no direct CP violating effects in the oscillation itself, which
is demonstrated by the exact solution, although it influences the neutron
electric dipole moment in the leading order of small $\Delta B=2$ parameters.
An analogue of Bogoliubov transformation, which preserves P and CP, is crucial
in the analysis.
