| $R\ \rightarrow\ (S\ v\ T)$ |
| $P\ v((S\ v\ T)\ \rightarrow\ W]$ |
| $M\ v\ \sim\ P$ |
| $(H\ \&\ N)\ \rightarrow\ \sim\ M$ |
| $H\ \&\ N$ |
| $(R\ \rightarrow\ W)\ v\ S$ |
| $(1)\ R\ \rightarrow\ (S\ v\ T)$ | $P$ |
| $(2)\ P\ v\ [(S\ v\ T)\ \rightarrow\ W)$ | $P$ |
| $(3)\ M\ v\ \sim\ P$ | $P$ |
| $(4)\ (H\ \&\ N)\ \rightarrow\ \sim\ M$ | $P$ |
| $(5)\ H\ \&\ N$ | $P/(R\ \rightarrow\ W)\ v\ S$ |
| $(6)\ \sim\ M$ | $4, 5, MP$ |
| $(7)\ \sim\ P$ | $3, 6, DS$ |
| $(8)\ (S\ v\ T) \rightarrow\ W$ | $2, 7, DS$ |
| $(9)\ R\ \rightarrow\ W$ | $1, 8, HS$ |
| $(10)\ (R\ \rightarrow\ W)\ v\ S$ | $9,$ Add. |
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| $(R\ \&\ S)\ v\ P$ |
| $P\ \rightarrow\ Q$ |
| $T\ v\ (R\ \&\ S)\ \rightarrow\ W ]$ |
| $S\ \&\ \sim\ T$ |
| $[S\ \&\ (W\ v\ Q)]\ v\ \sim\ P$ |
| $(X \rightarrow Y)\ v\ D$ |
| $A \rightarrow [(X \rightarrow Y) \rightarrow R]$ |
| $D \rightarrow E$ |
| $(E\ v\ F) \rightarrow A$ |
| $E\ v\ F$ |
| $\therefore (R\ v\ E)\ \&\ A$ |
| $(A\ v\ B) \rightarrow D$ |
| $A$ |
| $\therefore (D\ \&\ A)\ v\ P$ |
| $P\ v\ Q$ |
| $R \rightarrow\sim P$ |
| $R\ \&\ S$ |
| $Q \rightarrow (R\ \&\ P)$ |
| $\therefore P\ v\ H$ |