In mathematical logic, the Law of Detachment says that if the following two statements are true:

(1) *If $p$, then $q$*.

(2) $p$

Then we can derive a third true statement:

(3)$q$.

**Example:**

If the following statements are true, use the Law of Detachment 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

1) If $p$, then $q$.

2) $q$.

So, by the Law of Detachment, we can deduce that $q$ is true. That is,

You live in the Southern Hemisphere.