 reserve x,y,z,t for object,X,Y,Z,W for set;
 reserve R,S,T for Relation;

theorem
 for x being object holds  id({x}) = {[x,x]}
proof let x be object;
  x in {x} by TARSKI:def 1;
  then [x,x] in id({x}) by RELAT_1:def 10; then
A1: {[x,x]} c= id {x} by ZFMISC_1:31;
  [:{x},{x}:] = {[x,x]} by ZFMISC_1:29;
  then id({x}) c= {[x,x]} by Lm2;
  hence thesis by A1;
end;
