| $(P\ \&\ Q) \rightarrow [(P \rightarrow R)\ \&\ S]$ |
| $(P\ \&\ Q)\ \&\ T$ |
| $R\ v\ W$ |
| $(1)\ ( P\ \&\ Q)\ \rightarrow [(P\ \rightarrow R)\ \&\ S]$ | $P$ |
| $(2)\ (P\ \&\ Q)\ \&\ T$ | $P/ R\ v\ W$ |
| $(3)\ P\ \&\ Q$ | $2,$ Simp. |
| $(4)\ (P\ \rightarrow\ R)\ \&\ S$ | $1, 3, MP$ |
| $(5)\ P \rightarrow R$ | $4,$ Simp. |
| $(6)\ P$ | $3,$ Simp. |
| $(7)\ R$ | $5, 6, MP$ |
| $(8)\ R\ v\ w$ | $7,$ Add. |
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| $(P\ v\ Q)\ \rightarrow\ (T\ v\ S)$ |
| $\sim\ N\ \& \sim\ M$ |
| $N\ v\ \sim\ (T\ v\ S)$ |
| $H\ \rightarrow\ (P\ v\ Q)$ |
| $\therefore \sim\ H\ \&\ \sim\ M$ |
| $N \rightarrow (\sim Z \rightarrow G)$ |
| $D \rightarrow [K\ v\ Y) \rightarrow M]$ |
| $(X\ v\ Y\ v\ \sim\ Z$ |
| $D\ \&\ N$ |
| $\therefore\ (M\ v\ G)\ v\ K$ |
| $(A\ v\ B)\ v\ Q$ |
| $(J\ v\ K)\ v\ R$ |
| $\sim\ R\ \&\ \sim\ Q$ |
| $\therefore\ (A\ v\ B)\ \&\ (J\ v\ K)$ |