| $(E\rightarrow F)\rightarrow H$ |
| $\sim J\ v (F\ \&\ G)$ |
| $F \rightarrow(H\rightarrow I)$ |
| $\sim\ \sim J$ |
| $G\ \&\ [(E\rightarrow F) \rightarrow I]$ |
| $(1)\ (E \rightarrow F) \rightarrow H$ | $P$ |
| $(2)\ \sim J\ v(F\ \&\ G)$ | $P$ |
| $(3)\ F \rightarrow (H \rightarrow I$ | $P$ |
| $(4)\ \sim\ \sim J$ | $P/G[(E \rightarrow F) \rightarrow I]$ |
| $(5)\ F\ \&\ G$ | $2, 4, DS$ |
| $(6)\ F$ | $5,$ Simp. |
| $(7)\ H \rightarrow I$ | $3, 6, MP$ |
| $(8)\ (E \rightarrow F) \rightarrow I$ | $1, 7, HS$ |
| $(9)\ G$ | $5,$ Simp. |
| $(10)\ G\ \&\ [(E \rightarrow F) \rightarrow I]$ | $9, 8,$ Conj. |
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| $(D \rightarrow Q)\ \&\ ( A\rightarrow B)$ |
| $Q\ \&\ A:$ |
| $\therefore (B\ v\ D)\ \&\ Q$ |
| $(F \rightarrow S)\ \&\ (R \rightarrow W)$ |
| $F\ \&\ R$ |
| $\therefore \sim S\ \&\ W$ |
| $P \rightarrow Q$ |
| $\sim Q\ v\ R$ |
| $\sim R$ |
| $\therefore (\sim P \& \sim R)\ v\ S$ |