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