User blog comment:LittlePeng9/First order oodle theory/@comment-5150073-20141102075753/@comment-1605058-20141102080926

Every valid FOST expression is equally valid as FOOT expression. For something other than that, we can have for example $$\neg(\exists a(a\in b))\land\exists x(y\in x\land x\in [b])$$, which says first that b is empty set, and then if y is element of x, which is an ordinal (i.e. element of [0], which is $$\text{Ord}$$).