document.write( "Question 1177235: Conditional proof
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Algebra.Com's Answer #805710 by math_helper(2461) $\"\"$ $\"About$

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document.write( "1. M-->(K-->L)      Premise
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document.write( "2. (LvN)--> J       Premise
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document.write( "// show M-->(K-->J)
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document.write( "3.:: M              Conditional Proof (CP) assumption #1
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document.write( "4.:: K-->L          3,1  Modus Ponens (MP)
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document.write( "5.:: K              CP assumption #2
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document.write( "6.:: L              5,4  MP
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document.write( "7.:: LvN            6  addition (ADD)  [ The free lunch of logic ]
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document.write( "8.:: J              7,2  MP
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document.write( "9.:: K-->J          5-8  CP
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document.write( "10.:: M-->(K-->J)   3-9  CP
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document.write( "11. M-->(K-->J)     3-10 CP  \r
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document.write( "// Notes
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document.write( "Line 3  says assume M is true
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document.write( "Line 4  shows if M is true then it follows  K-->L  by Premise #1
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document.write( "Line 5  says assume K is true
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document.write( "Line 9  shows the if K is true then J is true (K-->J)
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document.write( "Line 10 just puts together \"if M true then it follows K-->J\"  so M-->(K-->J)
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document.write( "Line 11 discharges CP assumptions and brings the conclusion into the main
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document.write( "         argument.\r
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