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!
Use the fact that $\displaystyle A=B \Leftrightarrow (A\subseteq B \text{ and } B\subseteq A)$
Then start by letting some $\displaystyle x\in A$ and you can show that $\displaystyle x\in C$
Then let some $\displaystyle y\in C$ and you can show $\displaystyle y\in A$