In mathematical logic, the Law of Detachment says that if the following two statements are true:
(1) If p, then q.
Then we can derive a third true statement:
If the following statements are true, use the Law of Syllogism to derive a new true statement.
1) If you are a penguin, then you live in the Southern Hemisphere.
2) You are a penguin.
Let p be the statement "you are a penguin", let q be the statement "you live in the Southern Hemisphere".
Then (1) and (2) can be written
2) If p, then q.
So, by the Law of Detachment, we can deduce that q is true. That is,
You live in the Southern Hemisphere.