Show that $\left(P\rightarrow Q\right) \wedge \left(Q\rightarrow R\right)$ is equivalent to $\left(P\rightarrow R\right) \wedge \left[\left(P\leftrightarrow Q\right) \vee \left(R\leftrightarrow Q\right)\right]$
After one page of expanding and collapsing the right hand side, I get as a result $$ \left(P\rightarrow Q\right) \wedge \left(Q\rightarrow P\right) \wedge \left(P\rightarrow R\right) $$
Can anybody help? Although this question has been marked as a duplicate, the linked page only provides a partial answer (one direction) and the other answer is in Polish notation which I am not familiar with.