Question 981871
~H is freed up in line 5. Then this is used to free up  (~T > R) and (E > F). After that, they are conjuncted to get  (~T > R) & (E > F). After which you use constructive dilemma.


<table border=1><tr><th>Number</th><th>Statement</th><th>Lines Used</th><th>Reason</th></tr><tr><td>1</td><td>H v (~T &gt; R)</td><td></td><td></td></tr><tr><td>2</td><td>H v (E &gt; F)</td><td></td><td></td></tr><tr><td>3</td><td>~T v E</td><td></td><td></td></tr><tr><td>4</td><td>~H &amp; D</td><td></td><td></td></tr><tr><td>:.</td><td>R v F</td><td></td><td></td></tr><tr><td>5</td><td>~H</td><td>4</td><td>Simplification</td></tr><tr><td>6</td><td>~T &gt; R</td><td>1,5</td><td>Disjunctive Syllogism</td></tr><tr><td>7</td><td>E &gt; F</td><td>2,5</td><td>Disjunctive Syllogism</td></tr><tr><td>8</td><td>(~T &gt; R) &amp; (E &gt; F)</td><td>6,7</td><td>Conjunction</td></tr><tr><td>9</td><td>R v F</td><td>8,3</td><td>Constructive Dilemma</td></tr></table>