let X be BCI-algebra; :: thesis: ( ( for X being BCI-algebra
for x, y being Element of X holds x \ (x \ y) = y \ (y \ x) ) implies the carrier of X = BCK-part X )
assume for X being BCI-algebra
for x, y being Element of X holds x \ (x \ y) = y \ (y \ x) ; :: thesis: the carrier of X = BCK-part X
then X is BCK-algebra by BCIALG_1:12;
hence the carrier of X = BCK-part X by Th25; :: thesis: verum