Hi

I am reading "Introduction to Set theory" by J.Donald Monk and while going through

some theorem there, I needed the following equivalence.

$\displaystyle (p\Leftrightarrow q)\wedge (r \Leftrightarrow q)\equiv (p\Leftrightarrow r)$

I want to know if this is true ? I think so. Any hints about proving this without using

truth tables. I would just convert this into combination of $\displaystyle \wedge$ and

$\displaystyle \vee$ .I tried to do that but couldn't get rid of $\displaystyle r$ .

Any pointers ?