theorem :: BCIALG_3:19

for X being non empty BCIStr_0 holds
( X is BCI-commutative BCI-algebra iff for x, y, z being Element of X holds
( ((x \ y) \ (x \ z)) \ (z \ y) = 0. X & x \ (0. X) = x & x \ (x \ y) = y \ (y \ (x \ (x \ y))) ) )