Law of Detachment

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) p

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.