A subset of B equal to ~ B subset of ~ A
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In mathematics, a set A is a subset of a set B if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be equal; if they are unequal, then A is a proper subset of B.
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You can conclude that A and B are the same set, A=B .
This is an important characterization of the abstract objects that we would like to call sets. So much so that no theory can be called a set theory if such characterization fails. In Zermelo-Fraenkel set theory (and others) this property is an axiom and is called the axiom of extensionality
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