Hypothetical Syllogism/Formulation 1/Proof 1

Theorem

 * $p \implies q, q \implies r \vdash p \implies r$

Proof

 * align="right" | 4 ||
 * align="right" | 3, 1
 * $q$
 * $\implies \mathcal E$
 * 3, 1
 * align="right" | 5 ||
 * align="right" | 3, 2
 * $r$
 * $\implies \mathcal E$
 * 4, 2
 * align="right" | 6 ||
 * align="right" | 1, 2
 * $p \implies r$
 * $\implies \mathcal I$
 * 3, 5
 * }
 * align="right" | 1, 2
 * $p \implies r$
 * $\implies \mathcal I$
 * 3, 5
 * }
 * }