Five-phase axiomatic system refers to axiomatizable five-phase abstract system in which the earth（ T）element

differs from the other four phases

and has 4 ordered pair expression. According to the generation and restriction cycle of the five phases and the integrate convention of the system

each expression of T element can deduces the only generation and restriction relationship of five-phase system（ quinquangular model of generation and restriction）

which can not only solve the controversial problem of generation and restriction relationship and uniqueness of five-phase in the level of abstract system

but also is conducive to form a new mathematical relation（ including generation and restriction of the major elements）

and embodying the mutual promotion of Chinese medicine and mathematics and science and the study method of taking Chinese medicine as principal and starting point.