theorem :: BCIALG_1:86

for X being non empty BCIStr_0 holds
( X is positive-implicative 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 \ y = ((x \ y) \ y) \ (y `) & (x \ (x \ y)) \ (y \ x) = ((y \ (y \ x)) \ (y \ x)) \ (x \ y) ) )