| $(D \rightarrow Q)\ \&\ ( A\rightarrow B)$ |
| $Q\ \&\ A:$ |
| $\therefore (B\ v\ D)\ \&\ Q$ |
| $(1)\ (D \rightarrow Q)\ \&\ (A \rightarrow B)$ | $P$ |
| $(2)\ Q\ \&\ A$ | $P/ \therefore (B\ v\ D)\ \&\ Q$ |
| $(3)\ A \rightarrow B$ | $1,$ Simp. |
| $(4)\ A$ | $2,$ Simp. |
| $(5)\ B$ | $3, 4, MP$ |
| $(6)\ B\ v\ D$ | $5,$ Add. |
| $(7)\ Q$ | $2,$ Simp. |
| $(8)\ (B\ v\ D)\ \&\ Q$ | $6, 7,$ Conj. |
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| $E\rightarrow H$ |
| $F\rightarrow (I\ v\ P)$ |
| $(E\ v\ F)\ \&\ \sim G$ |
| $H \rightarrow G$ |
| $\therefore I\ v\ P$ |
| $(K\ \rightarrow\ L)\ \&\ 0$ |
| $\sim\ A\ \rightarrow\ (B\ \rightarrow\ C)$ |
| $A\ v\ (B\ v\ K)$ |
| $\sim\ A$ |
| $C\ v\ L$ |
| $G \rightarrow J$ |
| $J \rightarrow K$ |
| $(G \rightarrow K) v (J \rightarrow L)$ |
| $L \rightarrow M$ |
| $\therefore (J \rightarrow M) v\ Q$ |
| $P \rightarrow (Q\ v\ R)$ |
| $P \rightarrow S$ |
| $P\ v\ T$ |
| $\sim T$ |
| $\therefore S\ \&\ (Q\ v\ R)$ |