1. V&P
2. ~M&N
3. (VvS)>(R>M)
4. (VvP)>(X>R)
/~X
5. ~(VvS)v(R>M) 3, Material Implication
6. (~V&~S)v(R>M) 5, DeMorgan
7. [~Vv(R>M)]&[~Sv(R>M)] 6, Distribution
8. ~Vv(R>M) 7, Simplification
9. V>(R>M) 8, Material Implication
10. V 1, Simplification
11. R>M 9,10, Modus Ponens
12. ~(VvP)v(X>R) 3, Material Implication
13. (~V&~P)v(X>R) 12, DeMorgan
14. [~Vv(X>R)]&[~Pv(X>R)] 13, Distribution
15. ~Vv(X>R) 14, Simplification
16. V>(X>R) 15, Material Implication
17. X>R 16,10, Modus Ponens
18. ~M>~R 11, Transposition
19. ~M 2, Simplification
20. ~R 18,19, Modus Ponens
21. ~R>~X 17, Transposition
22. ~X 21,20, Modus Ponens
Edwin
