Is this a sound inference rule?

$$((p \land q) \rightarrow r) \land \lnot(p \rightarrow r)) \rightarrow (q \rightarrow r)$$

So far I've rewritten it to 
$$((p \rightarrow r) \land \lnot(p \rightarrow r)) \rightarrow (q \rightarrow r)$$ 

It looks similar to the syllogism rule, but I'm not sure. Any help?