| $(D \rightarrow Q)\ \&\ ( A\rightarrow B)$ |
| $Q\ \&\ A:$ |
| $\therefore (B\ v\ D)\ \&\ Q$ |
| $(1)\ (D \rightarrow Q)\ \&\ (A \rightarrow B)$ | $P$ |
| $(2)\ Q\ \&\ A$ | $P/ \therefore (B\ v\ D)\ \&\ Q$ |
| $(3)\ A \rightarrow B$ | $1,$ 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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| $N \ \&\ M$ |
| $\sim S\ (T \ \&\ W)$ |
| $(P \ \&\ R)\ v\ \sim S$ |
| $(N \ \&\ M) \rightarrow \sim (T \ \&\ W)$ |
| $(R \ \&\ N)\ v\ S$ |
| $\sim (A \ \&\ B) \rightarrow H$ |
| $F\ v \sim (H \ \&\ F)$ |
| $(A \ \&\ B) \rightarrow (H \ \&\ F)$ |
| $\sim F \ \&\ (D \ \&\ E)$ |
| $(D \ \&\ E) \ \&\ H$ |
| $\sim P\ \&\ (Q\ v\ R)$ |
| $(Q \rightarrow A)\ \&\ (R \rightarrow B)$ |
| $(A\ v\ B) \rightarrow (P\ v\ R)$ |
| $R$ |
| $A \rightarrow B$ |
| $A\ v\ C$ |
| $E\ \&\ \sim F$ |
| $\sim B$ |
| $\therefore\ C\ \&\ \sim F$ |