theorem Th96:
  x .--> x = id{x}
proof
  for y,z being object holds [y,z] in x .--> x iff y in {x} & y = z
  proof
    let y,z be object;
A1: x .--> x = {[x,x]} by ZFMISC_1:29;
    thus [y,z] in x .--> x implies y in {x} & y = z
    proof
      assume [y,z] in x .--> x;
      then
A2:   [y,z] = [x,x] by A1,TARSKI:def 1;
      then y = x by XTUPLE_0:1;
      hence thesis by A2,TARSKI:def 1,XTUPLE_0:1;
    end;
    assume y in {x};
    then y = x by TARSKI:def 1;
    hence thesis by A1,TARSKI:def 1;
  end;
  hence thesis by RELAT_1:def 10;
end;
