theorem Th1: :: BCIALG_1:1

for X being non empty BCIStr_0 holds
( X is BCI-algebra iff ( X is being_I & X is being_BCI-4 & ( for x, y, z being Element of X holds
( ((x \ y) \ (x \ z)) \ (z \ y) = 0. X & (x \ (x \ y)) \ y = 0. X ) ) ) )