Trying to write the proof and am stuck.
1.H > J
2.~(J & H) / ~H
==================================
1. H—>J Premise
2. ~(J & H) Premise
3. ~J v ~H 2, DeMorgan's (DeM)
4.:: ~J Conditional proof (CP), assumption #1
5.:: ~H 4,1 Modus Tollens (MT), end case #1
6.:: ~H Conditional proof, assumption #2, end case #2 (tautology ~H —> ~H)
7. (~J v ~H) —> ~H End CP, Proof by Cases (PBC) (if ~J or ~H we can conclude ~H)
8. ~(J & H) —> ~H 7, DeM
9. ~H 2,8 Modus Ponens (MP)
Other approaches may be possible.