Proof of proveit.logic.sets.enumeration.false_for_one_is_false_for_all theorem

import proveit
theory = proveit.Theory() # the theorem's theory

%proving false_for_one_is_false_for_all

With these allowed/disallowed theorem/theory presumptions (e.g., to avoid circular dependencies), we begin our proof of
false_for_one_is_false_for_all:
(see dependencies)