The hypothetical syllogism is a valid logical argument consisting of two premises and a conclusion, which altogether are constructed from three propositions $p,q$ and $r$ as follows:
Formally, the hypothecal syllogism is the following logical argument: $$\begin{array}{rll} p\Rightarrow q&\text{major premise}&\text{e.g. If it is raining then the roads are wet.}\\ q\Rightarrow r&\text{minor premise}&\text{e.g. If the roads are wet then they are slippery.}\\ \hline p\Rightarrow r&\text{conclusion}&\text{e.g. If it is raining, then the roads are slippery.}\\ \end{array} $$
Proofs: 1