Don't skip a space just after "(" or "[" and don't skip a space
just before ")" or "]". It looks confusing when you do.
Since by exportation the conclusion P ⊃ (M ⊃ W) is
equivalent to (P • M) ⊃ W, we will assume P • M for
a conditional proof
1. P ⊃ [(L v M) ⊃ (N • O)]
2. (O v T) ⊃ W / P ⊃ (M ⊃ W), same as (P • M) ⊃ W
|3. P • M ACP
|4. P 3, Simplification
|5. (L v M) ⊃ (N • O) 1,4, Modus ponens
|6. M • P 3, Commutation
|7. M 6, Simplification
|8. M v L 7, Addition
|9. L v M 8, Commutation
|10. N • O 5,9 Modus ponens
|11. O • N 10, Commutation
|12. O 11, Simplification
|13. O v T 12, Addition
|14. W 2,13, Modus ponens
15. (P • M) ⊃ W lines 3-14 Conditional proof.
16. P ⊃ (M ⊃ W) 15, Exportation
Edwin
