Hypothetical syllogism
A
hypothetical syllogism is a
valid argument of the following
form:
 P → Q.
 Q → R.
 Therefore, P → R.
In logical operator notation


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.