Dear Jumico:

First, you must understand the rule. The premise says if P then R... Therefore, whenever you have P then R should follow... Many logical fallacies are committed because we tend to ADD crucial operative words that change the meaning of premises drastically. For instance, some people tend to read the premise as If ONLY P then R, which is obviously different.

So, whenever you have P (whether alone or with conjunction of others) you must have R.

If P then R
Therefore if P and Q then R

Note that the above argument may be expressed as follows:

If P then R
It is P and Q
Therefore it is R
----------------

This said, here is the proof:

If P and Q
Then it is P*

Now replace the conclusion above (It is P) in the original argument with (If P and Q):

If P then R
It is P
Therefore it is R

* Of course it is also: "Then it is Q". But this is not relevant for this proof.

I hope this helps

Peace,
Edip

Thank you but it's not exactly what I'm looking for. I know how it works and I could prove it with words but I'm supposed to prove it with these 19 rules of inference. Somehow I need to use the rules to add in the q and get it to look right. Thank you I do appreciate the help. I'm going to look more in my book when I have access to it Friday.

I think your post gave me an idea. I'll post back later.

S'alright, many have called me logic proof too.