Using the Corollary 17A, if $\Sigma\vDash\tau$ , then there is a finite $\Sigma'=\{\alpha_{1},\ldots,\alpha_{n}\}\subseteq\Sigma$ such that $\Sigma'\vDash\tau$ . We start the deduction by listing all wffs $\alpha_{i}$ , $i=1,\ldots,n$ . Then, suppose that $\beta$ and $\gamma$ are already listed in the deduction, then we can add the tautology $(\beta\rightarrow(\gamma\rightarrow(\beta\wedge\gamma)))$ , then, using rule (c), $(\gamma\rightarrow(\beta\wedge\gamma))$ , and, using it again, $\beta\wedge\gamma$ . This way we can add $(\alpha_{1}\wedge\alpha_{2})$ , then $((\alpha_{1}\wedge\alpha_{2})\wedge\alpha_{3})$ etc. Finally, we have $(((\alpha_{1}\wedge\alpha_{2})\wedge\ldots)\wedge\alpha_{n})$ which is satisfied by a truth assignment $v$ iff $\Sigma'$ is satisfied by $v$ . Hence, $((((\alpha_{1}\wedge\alpha_{2})\wedge\ldots)\wedge\alpha_{n})\rightarrow\tau)$ is a tautology which can be further added, followed by $\tau$ (using again (c)).