Addition is also one of the rules of propositional logic. And it's a strange one.
P
Therefore, P∨Q (P or Q)
I have an apple, therefore I have an apple or an orange. Obviously true, but not generally useful. Note that having this rule means that if you have managed to show both P and ¬P (not P), you can proove anything.
P
P OR I am God (by addition)
¬P
Therefore, I am God.
This is also called disjunction introduction, although one cannot introduce the disjunction 'and' in the same way one can introduce 'or'.
Back up to Rules of Inference
Review your Logic symbols