Hypothetical syllogism

A hypothetical syllogism is a valid argument of the following form:

P ⇒ Q.

Q ⇒ R.

Therefore, P ⇒ R.

In other words, this kind of argument states that if one implies another, and that other implies a third, then the first implies the third. An example hypothetical syllogism:

If I do not wake up, then I cannot go to work.

If I cannot go to work, then I will not get paid.

Therefore, if I do not wake up, then I will not get paid.

See also syllogism, disjunctive syllogism.