reserve A,B,C,O for Ordinal,
        X for set,
        o for object,
        x,y,z,t,r,l for Surreal;

theorem
  x == y implies {x} <=_ {y}
proof
  assume A1:x == y;
  let z such that A2:z in {x};
  take y,y;
  thus thesis by A1,A2,TARSKI:def 1;
end;
