1.  (H v K) ⊃ (L v K)    Premise

2.  M ⊃ [H⊃ (N • ~L)]    Premise   

// Show  (M • H) ⊃ (N • K)

3.:: M • H               Conditional Proof (CP) assumption #1

4.:: M                   3, Simplification (SIMP)

5.:: H⊃ (N • ~L)         4,2  Modus Ponens (MP)

6.:: H                   3, SIMP

7.:: N • ~L              6,5 MP

8.:: N                   7, SIMP

9.:: ~(H v K) v (L v K)    1, Material Implication (MI)

10.:: (~H • ~K) v (L v K)  10, DeMorgan's (DM)  

11.:: ~L                 7, SIMP

12.:: H v K              6, Addition (ADD)

13.:: L v K              12,1  MP

14.:: K                  11,13 Disjunctive Syllogism (DS)

15.:: N • K              8,14 Conjunction (CONJ)

16. (M • H) ⊃ (N • K)    3-15, CP

 

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