I have the standard logical equivalence: $(p\rightarrow q)\wedge(q\rightarrow r)\Leftrightarrow p\rightarrow (q\wedge r)$.
Using several distributive laws I was able to get it down to: $(\neg p\wedge\neg q) \vee (\neg p\wedge r) \vee (q\wedge r)$.
I must be missing some manipulation I can do to reduce this.