Question 1031311
1.  ∀x(~(Fx v Gx) -> Hx) ----------Hypothesis
2.  ~(Fx v Gx) -> Hx   ------------------Universal instantiation
3.  ∀x(Hx -> Lx)  ---- ----------------Hypo.
4.  Hx -> Lx    -------------------------Universal instantiation
5.  ~(Fx v Gx) -> Lx  -------------------Hypothetical syllogism on #2 and #4
6.   (~Fx∩~Gx) -> Lx  ------------------- de Morgan's law
7.   ~Fx -> (~Gx-> Lx)  ---------------- Exportation
8.  ∀x(~Fx)  ---------------------------Hypo.
9.  ~Fx              -----------------------Universal instantiation
10.  ~Gx-> Lx   -------------------------Modus ponens on #7 and #9
11.  ~~Gx v Lx   -------------------------Material implication
12. Gx v Lx    ---------------------------Double negation
13. ∀x(Gx v Lx)   -----------------------Universal generalization