theorem
  (for X being BCI-algebra,x,y being Element of X holds x\(y\x)=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)=x;
  then X is BCK-algebra by BCIALG_1:14;
  hence thesis by Th25;
end;
