| $H \rightarrow ( I\ \&\ \sim J)$ |
| $( I\ v\ G) \rightarrow K$ |
| $H$ |
| $\sim K\ \&\ I$ |
| $(1)\ H \rightarrow(I\ \&\ \sim J)$ | $P$ |
| $(2)\ (I\ v\ G) \rightarrow K$ | $P$ |
| $(3)\ H$ | $P/ K\ \&\ I$ |
| $(4)\ I\ \& \sim\ J$ | $1, 3, MP$ |
| $(5)\ I$ | $4,$ Simp. |
| $(6)\ I\ v\ G$ | $5,$ Add. |
| $(7)\ K$ | $2, 6, MP$ |
| $(8)\ K\ \&\ I$ | $7, 5,$ Conj. |
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| $P\ v\ Q$ |
| $R \rightarrow \sim P$ |
| $R\ \&\ S$ |
| $Q \rightarrow (R\ \&\ P)$ |
| $\therefore P\ v\ R$ |
| $(A\ \&\ B)\ \rightarrow\ P$ |
| $\sim\ P\ \&\ \sim\ Q$ |
| $(J\ \rightarrow\ K)\ \rightarrow\ Q$ |
| $\sim\ (A\ \&\ B)\ \&\ \sim\ (J\ \rightarrow\ K)$ |
| $(R\ S) \rightarrow (F\ E)$ |
| $\sim (R\ S) \rightarrow J$ |
| $(F\ E) \rightarrow \sim H$ |
| $\sim\ \sim H$ |
| $\therefore \sim (J\ v\ G) \& \sim\ \sim H$ |
| $M \rightarrow N$ |
| $N \rightarrow O$ |
| $(M \rightarrow O) \rightarrow (N \rightarrow P)$ |
| $(N \rightarrow P) \rightarrow Q$ |
| $(Q\ v\ Z)\ \&\ Q$ |