The systematic theory about the relation between the neighboring phase regions (NPRs) and their boundaries in P-T-X_i multicomponent phase diagrams has been worked out. But three basic formulas about the relation between the dimension of boundary R_1’ and the dimension of phase boundary (PB) R_1 remain to be proved. Now we prove them theoretically, so our theory becomes more rigorous. The systematic theory about the relation between the neighboring phase regions (NPRs) and their boundaries in PT-X_i multicomponent phase diagrams has been worked out. But three basic formulas about the relation between the dimension of boundary R_1 ’and the dimension of phase boundary PB) R_1 remain to be proved. Now we prove them theoretically, so our theory has more rigorous.