@Srap Tasmaner@andrewk@Nagase or anyone else

1. All living things suffer
2. No living thing wants to suffer
3. No living thing that doesn't want to suffer wants to live
Therefore,
4. No living thing wants to live

Lx = x is a living thing, Sx = x has to suffer, Wx = x wants to live

Translating premises and conclusion in sequence:

1. (x)(Lx > Sx)
2. (x)(Lx > ~Wx)
3. (x)(~Wx > ~Lx)................/~(Ex)(Lx)
4. (Ex)(Lx).............................assume for reductio
5. Ly > ~Wy...........................2 UI
6. ~Wy > ~Ly.........................3 UI
7. Ly > ~Ly.............................5, 6 HS
8. La.......................................4 EG
9. (x)(Lx > ~Lx).....................7 UG
10. La > ~La..........................9 UI
11. ~La..................................8, 10 MP
12. La & ~La..........................8, 11 Conj
13. ~(Ex)(Lx).........................4 to 12 reductio

Is my proof good?

Why is premise 1 redundant? It seems necessary in the English language argument?