| $A \rightarrow B$ |
| $\sim B\ v\ D$ |
| $\sim D$ |
| $\therefore \sim A\ \&\ \sim D$ |
| $(1)\ A \rightarrow B$ | $P$ |
| $(2)\ \sim B\ v\ D$ | $P$ |
| $(3)\ \sim D$ | $P/\therefore \sim A\ \&\ \sim D$ |
| $(4)\ \sim B$ | $2, 3, DS$ |
| $(5)\ \sim A$ | $1, 4, MT$ |
| $(6)\ \sim A\ \&\ \sim D$ | $5, 3,$ Conj. |
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| $(P\ v\ R)\ \rightarrow (S\ v\ T)$ |
| $\sim M\ \&\ \sim N$ |
| $N\ v \sim (S\ v\ T)$ |
| $H \rightarrow (P\ v\ R)$ |
| $[\sim H\ \&\ \sim (P\ v\ R)]\ v\ S$ |
| $(K\ \rightarrow\ L)\ \&\ 0$ |
| $\sim\ A\ \rightarrow\ (B\ \rightarrow\ C)$ |
| $A\ v\ (B\ v\ K)$ |
| $\sim\ A$ |
| $C\ v\ L$ |