# Math Help - Set Theory Transitivity Proof

1. ## Set Theory Transitivity Proof

Hey all, how can we prove the following proposition about set theory?

Let A,B,C be sets.

If A=B and B=C then A=C

Thanks!

2. ## Re: Set Theory Transitivity Proof

Use the fact that $A=B \Leftrightarrow (A\subseteq B \text{ and } B\subseteq A)$

Then start by letting some $x\in A$ and you can show that $x\in C$

Then let some $y\in C$ and you can show $y\in A$