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 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

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

2) *p*.

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

You live in the Southern Hemisphere.