reserve X for BCI-algebra;
reserve x,y,z,u,a,b for Element of X;
reserve IT for non empty Subset of X;

theorem Th9:
  (x\y)` = x`\y`
proof
  x`\y`= ((((x\y)\(x\y))\x)\y`) by Def5
    .= ((((x\y)\x)\(x\y))\y`) by Th7
    .= ((((x\x)\y)\(x\y))\y`) by Th7
    .= ((y`\(x\y))\y`) by Def5
    .= (y`\y`)\(x\y) by Th7;
  hence thesis by Def5;
end;
