I think that this is a common Not IN. That is, for example, write:
select * from table1 where some_id NOT IN (select some_id from table2 where some_conditon)
In a nested select just list all the values you need many - this will be the quantifier FORALL. But taking the negation NOT IN - will be the negation of the quantifier FORALL and as a result of the implementation of the FORALL quantifier NOT.