Question 1132243
Here is one way to do a proof derivation to get the conclusion
<table border=1><tr><th>Number</th><th>Statement</th><th>Lines Used</th><th>Reason</th></tr><tr><td>1</td><td>R v ~S</td><td></td><td></td></tr><tr><td>2</td><td>~R v T</td><td></td><td></td></tr><tr><td>3</td><td>T --&gt; (S &amp; U)</td><td></td><td></td></tr><tr><td>:.</td><td>S = T</td><td></td><td></td></tr><tr><td>4</td><td>~S v R</td><td>1</td><td>Commutation</td></tr><tr><td>5</td><td>~~S --&gt; R</td><td>4</td><td>Material Implication</td></tr><tr><td>6</td><td>S --&gt; R</td><td>5</td><td>Double Negation</td></tr><tr><td>7</td><td>~~R --&gt; T</td><td>2</td><td>Material Implication</td></tr><tr><td>8</td><td>R --&gt; T</td><td>7</td><td>Double Negation</td></tr><tr><td>9</td><td>S --&gt; T</td><td>6,8</td><td>Hypothetical Syllogism</td></tr><tr><td>10</td><td>~T v (S &amp; U)</td><td>3</td><td>Material Implication</td></tr><tr><td>11</td><td>(~T v S) &amp; (~T v U)</td><td>10</td><td>Distribution</td></tr><tr><td>12</td><td>~T v S</td><td>11</td><td>Simplification</td></tr><tr><td>13</td><td>~~T --&gt; S</td><td>12</td><td>Material Implication</td></tr><tr><td>14</td><td>T --&gt; S</td><td>13</td><td>Double Negation</td></tr><tr><td>15</td><td>(S --&gt; T) &amp; (T --&gt; S)</td><td>9,14</td><td>Conjunction</td></tr><tr><td>16</td><td>S = T</td><td>15</td><td>Material Equivalence</td></tr></table>