Question 1193420
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Derivation Table
<table border = "1" cellpadding = "5"><tr><td colspan=2>Number</td><td>Statement</td><td>Line(s) Used</td><td>Reason</td></tr><tr><td>1</td><td></td><td>~A -> (B & C)</td><td></td><td></td></tr><tr><td>2</td><td></td><td>D -> ~C</td><td></td><td></td></tr><tr><td></td><td>:.</td><td>D -> A</td><td></td><td></td></tr><tr><td></td><td>3</td><td>D</td><td></td><td>Assumption for Conditional Proof</td></tr><tr><td></td><td>4</td><td>~C</td><td>2,3</td><td>Modus Ponens</td></tr><tr><td></td><td>5</td><td>~C v ~B</td><td>4</td><td>Addition</td></tr><tr><td></td><td>6</td><td>~B v ~C</td><td>5</td><td>Commutation</td></tr><tr><td></td><td>7</td><td>~(B & C)</td><td>6</td><td>De Morgan’s Law</td></tr><tr><td></td><td>8</td><td>~~A</td><td>1,7</td><td>Modus Tollens</td></tr><tr><td></td><td>9</td><td>A</td><td>8</td><td>Double Negation</td></tr><tr><td>10</td><td></td><td>D -> A</td><td>3-9</td><td>Conditional Proof</td></tr></table>


In line 3, I have the antecedent D as the assumption to start the conditional proof off. 
We simply start with the "if" part of the "if, then" conditional in the conclusion.
So we assume that the logical statement D is the case. 
Somehow we have to arrive at statement A based on this key assumption.


That's exactly what this derivation table does. The proof more or less starts at line 3, while working its way down until reaching line 9 where we arrive at statement A. 
Collectively lines 3 through 9 all group together to show D leading to A, therefore D -> A


I'm using arrow symbols in place of the horseshoe symbols.
Also, I used ampersands in place of the dot symbols.
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