document.write( "Question 1159126: D ⊃ (F • S) / (B ⊃ D) ⊃ (B ⊃ S)\r
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Algebra.Com's Answer #782125 by Edwin McCravy(20055)\"\" \"About 
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document.write( "     D  ⊃ (F • S)       / (B ⊃ D) ⊃ (B ⊃ S)\r\n" );
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document.write( "This one is a little different.  We first find a conditional statement which is\r\n" );
document.write( "equivalent to the conclusion.  Then we do a conditional proof on the equivalent\r\n" );
document.write( "statement and then the conclusion will follow.\r\n" );
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document.write( "Exportation says that p ⊃ (q ⊃ r) and (p • q) ⊃ r are equivalent.  Let's\r\n" );
document.write( "substitute (B ⊃ D) for p, B for q, and S for r.  Then we have this\r\n" );
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document.write( " (B ⊃ D) ⊃ (B ⊃ S)  <=> [(B ⊃ D) • B] ⊃ S\r\n" );
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document.write( "Now we know what to assume, which is the left side of the equivalent\r\n" );
document.write( "statement to the conclusion: (B ⊃ D) • B\r\n" );
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document.write( " 1.  D ⊃ (F • S)        / (B ⊃ D) ⊃ (B ⊃ S) \r\n" );
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document.write( "                        | 2. (B ⊃ D) • B    Assumption for conditional proof\r\n" );
document.write( "                        | 3. B ⊃ D          2, simplification\r\n" );
document.write( "                        | 4. B • (B ⊃ D)    2, commutation\r\n" );
document.write( "                        | 5. B              4, simplification\r\n" );
document.write( "                        | 6. D              3,5, modus ponens\r\n" );
document.write( "                        | 7. F • S          1,6, modus ponens\r\n" );
document.write( "                        | 8. S • F          7, commutation\r\n" );
document.write( "                        | 9. S              8, simplification\r\n" );
document.write( "10. [(B ⊃ D) • B] ⊃ S   lines 2--9  by conditional proof\r\n" );
document.write( "11. (B ⊃ D) ⊃ (B ⊃ S)   10, exportation\r\n" );
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document.write( "Edwin
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