| $B\ \&\ (A\ v\ D)$ |
| $(A \rightarrow E)\ \&\ (D \rightarrow F)$ |
| $(E\ v\ F) \rightarrow (B\ v\ D)$ |
| $\sim B$ |
| $D$ |
| $(1)\ B\ \&\ (A\ v\ D)$ | $P$ |
| $(2)\ (A \rightarrow E)\ \&\ (D \rightarrow F)$ | $P$ |
| $(3)\ (E\ v\ F) \rightarrow (B\ v\ D)$ | $P$ |
| $(4)\ \sim B$ | $P/ D$ |
| $(5)\ A\ v\ D$ | $1,$ Simp. |
| $(6)\ A \rightarrow E$ | $2,$ Simp. |
| $(7)\ D \rightarrow F$ | $2,$ Simp. |
| $(8)\ E\ v\ F$ | $6, 7, 5, CD$ |
| $(9)\ B\ v\ D$ | $3, 8, MP$ |
| $(10)\ D$ | $9, 4, DS$ |
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| $(A\ \rightarrow\ B)\ v\ D$ |
| $H\ \rightarrow\ [(A \ \rightarrow\ B)\ \rightarrow\ R]$ |
| $D\ \rightarrow\ E$ |
| $(E\ v\ F)\ \rightarrow\ H$ |
| $E\ v\ F$ |
| $(R\ v\ E)\ \&\ H$ |
| $(P\ \&\ R)\ \&\ \sim T$ |
| $T\ v\ (F\ \&\ G)$ |
| $(F\ \&\ G )\ \rightarrow\ H$ |
| $\therefore (H\ \&\ P)\ v\ F$ |