In the self-consistent dual unitarization model with several input Regge trajectories we prove that: i) the intercept of output Pomeron pole is exactly equal to one, i. e. α_P(0)=1, ii) equal spacing rules hold for the intercepts of the Regge trajectories, i. e. [numerical formula], [numerical formula], [numerical formula], iii) SU(4) symmetric coupling constant g^2 satisfies the relation [numerical formula]. The proof for these consequences is given by allowing in the loops of the unitarity sum all the possible Regge trajectories and assuming exact SU(4) symmetry for the Reggeon coupling constants, while broken SU(4) symmetry for the intercepts of the Regge trajectories. The positions of the daughter trajectories for the Pomeron and the Regge trajectories are also discussed numerically