Question 1041461
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I'm going to use a conditional proof

<table border=1 cellpadding=3><tr><th colspan="2">Number</th><th>Statement</th><th>Lines Used</th><th>Reason</th></tr><tr><td>1</td><td></td><td>~S -&gt; (F -&gt; L)</td><td></td><td></td></tr><tr><td>2</td><td></td><td>F -&gt; (L -&gt; P)</td><td></td><td></td></tr><tr><td>:.</td><td></td><td>~S -&gt; (F -&gt; P)</td><td></td><td></td></tr><tr><td>|</td><td>3</td><td>~S</td><td></td><td>ACP</td></tr><tr><td>|</td><td>4</td><td>F -&gt; L</td><td>1,3</td><td>MP</td></tr><tr><td>|</td><td>5</td><td>(F &amp; L) -&gt; P</td><td>2</td><td>Exp</td></tr><tr><td>|</td><td>6</td><td>(L &amp; F) -&gt; P</td><td>5</td><td>Comm</td></tr><tr><td>|</td><td>7</td><td>L -&gt; (F -&gt; P)</td><td>6</td><td>Exp</td></tr><tr><td>|</td><td>8</td><td>F -&gt; (F -&gt; P)</td><td>4,7</td><td>HS</td></tr><tr><td>|</td><td>9</td><td>(F &amp; F) -&gt; P</td><td>8</td><td>Exp</td></tr><tr><td>|</td><td>10</td><td>F -&gt; P</td><td>9</td><td>Taut</td></tr><tr><td>11</td><td></td><td>~S -&gt; (F -&gt; P)</td><td>3-10</td><td>CP</td></tr></table>


Abbreviations/Acronyms Used:
ACP = Assumption for Conditional Proof
CP = Conditional Proof
Comm = Commutation
Exp = Exportation
HS = Hypothetical Syllogism
MP = Modus Ponens
Taut = Tautology
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