theorem
  (for X being BCI-algebra,x,y being Element of X holds (x\y)\((x\y)\(y\
  x))=0.X) implies the carrier of X = BCK-part(X)
proof
  assume for X being BCI-algebra,x,y being Element of X holds (x\y)\((x\y)\(y
  \x))=0.X;
  then X is BCK-algebra by BCIALG_1:17;
  hence thesis by Th25;
end;
