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Without the axiom that defines 
there would be
little point in defining the integers or anything else. The axiom
of extensionality says sets are uniquely defined by their
members.
means 
and 
have the same truth value or are
equivalent. They are either both true or both false. It is the same
as
. This
axiom says a pair of sets 
and 
are equal if and only if they have exactly the same members.
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