In this article the general theory of Commutative BCK-algebras and BCI-algebras and several classes of BCK-algebras are given according to .
 Yuzhong Ding. Several classes of BCI-algebras and their properties. Formalized Mathematics, 15(1):1-9, 2007.
 Jie Meng and YoungLin Liu. An Introduction to BCI-algebras. Shaanxi Scientific and Technological Press, 2001.
 Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
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