Hypothetical Syllogism

Theorem
The (rule of the) hypothetical syllogism is a valid deduction sequent in propositional logic:


 * If we can conclude that $p$ implies $q$, and if we can also conclude that $q$ implies $r$, then we may infer that $p$ implies $r$.

Also known as
It is referred to by some authors as the principle of syllogism

It is also known as the transitivity law.

Its abbreviation in a tableau proof is $\textrm{HS}$.