Simplification (AKA 'simp') is one of the rules in propositional logic. It is very simple, but one of the strengths of propositional logic is that it makes even the most simple parts of a logical argument explicit. Simplification goes thuswise:

P∧Q (P and Q)

Therefore, P

But beware! If you are being completely orthodox, you cannot say that:

P∧Q

Therefore,Q

If you want Q, you have to use Commutativity first, to get Q∧P.

P and Q represent any statements. For example, "there are cats AND there are dogs, therefore there are cats."

See also the rule of Addition, which is essentially the reverse of the rule of simplification.

Back up to Rules of Inference

Review your Logic symbols