摘要
证明了Ｈｉｌｂｅｒｔ代数（Ｈ，→，１）是反正蕴涵的ＢＣＫ－代数，即若使ａ＊ｂ＝ｂ→ａ，则（Ｈ，＊，１）是正蕴涵ＢＣＫ－代数。１在（Ｈ，→，１）中是最大元，而在（Ｈ，＊，１）中是最小元。
We have proved that every Hilbert algebras (H,→,1) are anti position implicative BCK algebras,that is, if a*b=b→a then (H,*,1) is a position implicative BCK algebras. At the same time, 1 is the largest element of (H,→,1) and it is also the smallest of (H,*,1).
