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Let $A,B \text{ and } C$ are three sets then if $ A \subset B, B \subset C, C \subset A \Rightarrow B = C $

How could we prove this ?

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    "Axioms" are not meant to be proven.2010-12-22
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    As you say sir.2010-12-22
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    @Damir Is this a homework assignment?2010-12-22
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    I know @Asaf; the reason for that comment is that the [previous version](http://math.stackexchange.com/posts/15188/revisions) of the question said that it was.2010-12-22
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    @J.M. whoops... I only saw that now.2010-12-22
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    Don't you mean $\subseteq$ rather than $\subset$?2010-12-22
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    @ Anthony Labarre: It is $\subset$.2010-12-22
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    @Anthony: both $\subset$ and $\subseteq$ usually mean subset or equal to, and $\subsetneq$ is used to denote proper inclusion.2010-12-22
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    Thanks for clarifying, Asaf, I'm used to different conventions.2010-12-22
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    @Anthony: Strictly speaking, $\subset$ should indeed mean proper inclusion, in analogy to $<$ meaning strictly less than. However, in this world this probably won't be accepted any more.2010-12-22
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    @Hendrik: I'm a TA in an introductory course in set theory, as I told my students on the first class: Some people use this notation and other use that notation. If you want to be absolutely clear use $\subseteq$ when the inequality is weak and $\subsetneq$ when it is strong. And since strong $\implies$ weak anyway, use the weak one when you're not certain.2010-12-22
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    @Asaf: I'm telling my students the same `:-)`2010-12-22
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    Aren't this also implies $A = B$ ?!2010-12-23

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