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