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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.