Question 1177235
<pre>
1. M-->(K-->L)      Premise
2. (LvN)--> J       Premise
// show M-->(K-->J)
3.:: M              Conditional Proof (CP) assumption #1
4.:: K-->L          3,1  Modus Ponens (MP)
5.:: K              CP assumption #2
6.:: L              5,4  MP
7.:: LvN            6  addition (ADD)  [ The free lunch of logic ]
8.:: J              7,2  MP
9.:: K-->J          5-8  CP
10.:: M-->(K-->J)   3-9  CP
11. M-->(K-->J)     3-10 CP  

// Notes
Line 3  says assume M is true
Line 4  shows if M is true then it follows  K-->L  by Premise #1
Line 5  says assume K is true
Line 9  shows the if K is true then J is true (K-->J)
Line 10 just puts together "if M true then it follows K-->J"  so M-->(K-->J)
Line 11 discharges CP assumptions and brings the conclusion into the main
         argument.