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 Th10:
  ((x\(x\y))\(y\x))\(x\(x\(y\(y\x))))=0.X
proof
  ((x\(x\y))\(y\x))\(x\(x\(y\(y\x)))) =((x\(x\y))\(x\(x\(y\(y\x)))))\(y\x)
  by Th7
    .=((x\(x\(x\(y\(y\x)))))\(x\y))\(y\x) by Th7
    .=((x\(y\(y\x)))\(x\y))\(y\x) by Th8
    .=((x\(y\(y\x)))\(x\y))\(y\(y\(y\x))) by Th8;
  hence thesis by Th1;
end;
