Question 1209282
<pre>
I am not sure what symbol you use for "and" ("conjunction") so I'll use "&"

1. ~(~Z v H) ⊃ ~T
2. (S ⊃ Z) ⊃ ~H   ∴  Z ⊃ ~T

3. ~~T ⊃ ~~(~Z v H)  1, transposition
4. T ⊃ (~Z v H)      4, double negation
5.                    | 5.  ~(Z ⊃ ~T)       Assumption for indirect proof
                      | 6.  ~(~~T ⊃ ~Z)     5, Transposition
                      | 7.  ~(T ⊃ ~Z)       6, Double negation
                      | 8.  ~(T ⊃ (~Z v H)) 7, Addition,                                  
                      | 9.  T ⊃ (~Z v H) & ~(T ⊃ (~Z v H))
                                            4,8, Conjunction
10. Z ⊃ ~T      lines 5-9 for indirect proof

Notice that premise 2 was not used or needed.

Edwin</pre>