Delete with join to multiple tables

Code:

create table coltype (coltype varchar(5));

insert into coltype values ('typ1');

create table colsubtype (coltype varchar(5), colsubtype varchar(5));

insert into colsubtype values ('typ2', 'st1');
insert into colsubtype values ('typ2', 'st2');

create table table1 (col1 varchar(5), coltype varchar(5), colsubtype varchar(5));

insert into table1 values ('val1','typ1', 'st1');
insert into table1 values ('val2','typ1', 'st2');
insert into table1 values ('val3','typ1', 'st3');
insert into table1 values ('val4','typ2', 'st1');
insert into table1 values ('val5','typ2', 'st2');
insert into table1 values ('val6','typ2', 'st3');
insert into table1 values ('val7','typ3', 'st1');
insert into table1 values ('val8','typ3', 'st2');
insert into table1 values ('val9','typ3', 'st3');

commit;

Basically, I want to delete all records where the coltype and colsubtype is not mentioned in the coltype and colsubtype tables.

How do I do that. The below is path I was thinking of taking but it does not work - and - it does not seem like a good design.

delete from table1 
where coltype != (select coltype from coltype) 
    OR not (coltype = cst.coltype and colsubtype = cst.colsubtype 
from (select coltype,  colsubtype from colsubtype) cst)