| $A \rightarrow B$ |
| $A\ v\ C$ |
| $E\ \&\ \sim F$ |
| $\sim B$ |
| $\therefore\ C\ \&\ \sim F$ |
| $(1)\ A \rightarrow B$ | $P$ |
| $(2)\ A\ v\ C$ | $P$ |
| $(3)\ E\ \&\ \sim F$ | $P$ |
| $(4)\ \sim B$ | $P/ \therefore\ C\ \&\ \sim F$ |
| $(5)\ \sim A$ | $1, 4, MT$ |
| $(6)\ C$ | $2, 5, DS$ |
| $(7)\ \sim F$ | $3,$ Simp. |
| $(8)\ C\ \&\ \sim F$ | $6, 7,$ Conj. |
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| $(P\ \&\ R)\ v\ \sim\ S$ |
| $(P\ \&\ R)\ \rightarrow\ \sim\ T$ |
| $M\ \rightarrow\ \sim\ \sim\ T$ |
| $M$ |
| $M\ \&\ \sim\ S$ |
| $(M\ v\ N)\ \&\ K$ |
| $[M\ v\ N)\ v\ L] \rightarrow H$ |
| $[( M\ v\ N)\ \&\ H] \rightarrow Z$ |
| $\therefore Z$ |
| $(H\ \&\ K)\ \rightarrow\ (J\ v\ K)$ |
| $\sim\ E\ \&\ \sim\ F$ |
| $F\ v\ \sim\ (J\ v\ K)$ |
| $\sim\ (H\ \&\ K)\ \rightarrow\ H$ |
| $H\ \&\ \sim\ E$ |