| $(A\ v\ B)\ \rightarrow\ D$ |
| $E\ \rightarrow\ \sim\ D$ |
| $(G\ \leftrightarrow\ F)\ \rightarrow\ (E\ \&\ H)$ |
| $G\ \leftrightarrow\ F$ |
| $\sim\ (A\ v\ B)\ \&\ H$ |
| $(1)\ (A\ v\ B)\ \rightarrow\ D$ | $P$ |
| $(2)\ E\ v\ \sim\ D$ | $P$ |
| $(3)\ (G\ \leftrightarrow\ F)\ \rightarrow\ (E\ \&\ H)$ | $P$ |
| $(4)\ G\ \leftrightarrow\ F$ | $P/\ \sim\ (A\ v\ B)\ \&\ H$ |
| $(5)\ E\ \&\ H$ | $3, 4, MP$ |
| $(6)\ E$ | $5,$ Simp. |
| $(7)\ \sim\ D$ | $2, 6, MP$ |
| $(8)\ \sim\ (A\ v\ B)$ | $1, 7, MT$ |
| $(9)\ H$ | $5,$ Simp. |
| $(10)\ \sim\ (A\ v\ B)\ \&\ H$ | $8, 9,$ Conj. |
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| $(A\ v\ B)\ v\ Q$ |
| $(J\ v\ K)\ v\ R$ |
| $\sim\ R\ \&\ \sim\ Q$ |
| $\therefore\ (A\ v\ B)\ \&\ (J\ v\ K)$ |
| $(Q\ \&\ B)\ v\ \sim D$ |
| $(Q\ \&\ B) \rightarrow \sim E$ |
| $F \rightarrow \sim\ \sim E$ |
| $\sim D \rightarrow (L\ \&\ N)$ |
| $F$ |
| $L\ v\ (B\ \&\ D)$ |
| $X \rightarrow Y$ |
| $Y \rightarrow Z$ |
| $(X \rightarrow Z) \rightarrow (Y \rightarrow P)$ |
| $(Y\ V\ P) \rightarrow Z$ |
| $\therefore Z\ v\ Q$ |