Can IS DISTINCT FROM be combined with ANY or ALL somehow?
Looking at it as a grammar problem, ANY is defined as
(in Row and Array Comparisons):


  expression operator ANY (array expression)


But is distinct from is not an operator, it's a "construct" as we're told in Comparison Operators:


  When this behavior is not suitable, use the IS [ NOT ] DISTINCT FROM
  constructs


Since PostgreSQL has user-defined operators, we may define an operator/function combo for this purpose:

create function is_distinct_from(text, text) returns bool as 
'select $1 is distinct from $2;' language sql;

create operator &lt;!&gt; (
 procedure=is_distinct_from(text,text),
 leftarg=text, rightarg=text
);


Then it can precede ANY:

select count(*)
from (select 'A' foo union all select 'Z' union all select null) z
where foo &lt;!&gt; any(array[null, 'A']);  



 count 
-------
     3
(1 row)