| $(A\ v\ D) \rightarrow (R\ \&\ S)$ |
| $E\ v\ (A\ v\ D)$ |
| $F\ \&\ \sim E$ |
| $(R\ \&\ F)\ v\ K$ |
| $(1)\ (A\ v\ D) \rightarrow (R\ \&\ S)$ | $P$ |
| $(2)\ E\ v\ (A\ v\ D)$ | $P$ |
| $(3)\ F\ \&\ \sim E$ | $P/ (R\ \&\ F)\ v\ K$ |
| $(4)\ \sim E$ | $3,$ Simp. |
| $(5)\ A\ v\ D$ | $2, 4, DS$ |
| $(6)\ R\ \&\ S$ | $1, 5, MP$ |
| $(7)\ R$ | $6,$ Simp. |
| $(8)\ F$ | $3,$ Simp. |
| $(9)\ R\ \&\ F$ | $7, 8,$ Conj. |
| $(10)\ (R\ \&\ F)\ v\ K$ | $9,$ Add. |
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| $(P \leftrightarrow Q) \rightarrow (A \leftrightarrow B)$ |
| $(R \ \&\ S)\ v\ (P \leftrightarrow Q)$ |
| $(F \ \&\ D) \rightarrow \sim\ (R \ \&\ S)$ |
| $(H \ \&\ G)\ v\ (F \ \&\ D)$ |
| $\sim (H \ \&\ G)$ |
| $(A \leftrightarrow B)\ v\ (B \leftrightarrow D)$ |
| $(P\ \&\ Q) \rightarrow [(P \rightarrow R)\ \&\ S]$ |
| $(P\ \&\ Q)\ \&\ T$ |
| $R\ v\ W$ |
| $E\ v\ (E\ \&\ Q)$ |
| $E \rightarrow L$ |
| $\sim L$ |
| $Q\ v\ M$ |
| $A \rightarrow B$ |
| $(A\ \&\ B) \rightarrow C$ |
| $A$ |
| $\therefore (A\ \&\ B)\ \&\ (A\ \&\ C)$ |
| $A \rightarrow B$ |
| $\sim B\ v\ D$ |
| $\sim D$ |
| $\therefore \sim A\ \&\ \sim D$ |
| (A & B) $\rightarrow$ [A $\rightarrow$ (D & E)] |
| (A & B) & C |
| $\therefore$E v G |