Not sure if this will click for you but here is a rough explanation of Law of Detachment
1) If you are a penguin, then you live in the Southern Hemisphere.
2) You are a penguin.
Let pp be the statement "you are a penguin", let qq be the statement "you live in the Southern Hemisphere".
Then (1) and (2) can be written
1) If pp , then qq .
2) pp .
So, by the Law of Detachment, we can deduce that qq is true. That is,
You live in the Southern Hemisphere.
