Are there rules of Logic dealing with the implies operator? I'm just beginning a course in discrete mathematics and I'm learning a few of the basic laws to prove propositions. I understand how to use propositions that use the logical connectives, AND , OR, NOT. However I'm not sure how to prove a proposition that has an implies operator. For example prove the following is a tautology.
$(p\land (p\implies q))\implies q$ 

There's a nice shortcut to proving that something with an implies operator is a tautology.  Assume it's not a tautology: the only way $a \Rightarrow b$ can be false is if $a$ is true and $b$ is false, so you can assume that, etc. and this is often a quick way to reach a contradiction.
