Create a new smartlist with:
Member of program = program name1 OR
Member of program = program name2 OR
Member of program = program name3
In the original already created smartlist, update from ALL or ANY filter logic to ADVANCED. Ommit all X filters. Add a new filter with Member of Smartlist and refer to the new smartlist. Update the filter logic with AND Y outside of the original filters. E.g. (1 and 2 and 3 and 4) and 5.
If filter 5 in your example is the Member of Smart List filter, and they want to add all of those leads in addition to the ones they already have, I believe you actually want OR before the 5:
(1 and 2 and 3 and 4) or 5
Otherwise it would require that all leads qualifying for the parent smart list also be in the new smart list.
Alternatively, you could add the 3 Member of Program filters to your original smart list:
(1 and 2 and 3 and 4) or 5 or 6 or 7