Law of detachment
If a conditional is true and its hypothesis is true, then its conclusion is true.
A real life example of the law of detachment
No one needs to be a rocket scientist to know that if the battery of a car is dead, then the car will not start. This is a knowledge that most of us have.
Now suppose a mechanic comes to your house and check the battery in your car and tell you that the battery is dead, what conclusion will you make? You will make the conclusion that your car will not start.
The statement ” If the battery of a car is dead, then the car will not start ” is a conditional statement.
Let p = the battery of a car is dead.
Let q = the car will not start.
We can write the conditional above as p → q
p → q is read if p, then q