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