Step |
Hyp |
Ref |
Expression |
1 |
|
meredith |
⊢ ( ( ( ( ( 𝜓 → 𝜓 ) → ( ¬ 𝜓 → ¬ 𝜓 ) ) → 𝜓 ) → 𝜓 ) → ( ( 𝜓 → 𝜓 ) → ( 𝜓 → 𝜓 ) ) ) |
2 |
|
meredith |
⊢ ( ( ( ( ( 𝜓 → 𝜓 ) → ( ¬ 𝜓 → ¬ ¬ ¬ 𝜑 ) ) → 𝜓 ) → 𝜑 ) → ( ( 𝜑 → 𝜓 ) → ( ¬ ¬ 𝜑 → 𝜓 ) ) ) |
3 |
|
merlem1 |
⊢ ( ( ( ( 𝜑 → 𝜓 ) → ( ¬ ¬ 𝜑 → 𝜓 ) ) → ¬ ( ( ( ( ( 𝜓 → 𝜓 ) → ( ¬ 𝜓 → ¬ 𝜓 ) ) → 𝜓 ) → 𝜓 ) → ( ( 𝜓 → 𝜓 ) → ( 𝜓 → 𝜓 ) ) ) ) → ( ¬ 𝜑 → ¬ ( ( ( ( ( 𝜓 → 𝜓 ) → ( ¬ 𝜓 → ¬ 𝜓 ) ) → 𝜓 ) → 𝜓 ) → ( ( 𝜓 → 𝜓 ) → ( 𝜓 → 𝜓 ) ) ) ) ) |
4 |
|
merlem4 |
⊢ ( ( ( ( ( 𝜑 → 𝜓 ) → ( ¬ ¬ 𝜑 → 𝜓 ) ) → ¬ ( ( ( ( ( 𝜓 → 𝜓 ) → ( ¬ 𝜓 → ¬ 𝜓 ) ) → 𝜓 ) → 𝜓 ) → ( ( 𝜓 → 𝜓 ) → ( 𝜓 → 𝜓 ) ) ) ) → ( ¬ 𝜑 → ¬ ( ( ( ( ( 𝜓 → 𝜓 ) → ( ¬ 𝜓 → ¬ 𝜓 ) ) → 𝜓 ) → 𝜓 ) → ( ( 𝜓 → 𝜓 ) → ( 𝜓 → 𝜓 ) ) ) ) ) → ( ( ( ( ( ( 𝜑 → 𝜓 ) → ( ¬ ¬ 𝜑 → 𝜓 ) ) → ¬ ( ( ( ( ( 𝜓 → 𝜓 ) → ( ¬ 𝜓 → ¬ 𝜓 ) ) → 𝜓 ) → 𝜓 ) → ( ( 𝜓 → 𝜓 ) → ( 𝜓 → 𝜓 ) ) ) ) → ( ¬ 𝜑 → ¬ ( ( ( ( ( 𝜓 → 𝜓 ) → ( ¬ 𝜓 → ¬ 𝜓 ) ) → 𝜓 ) → 𝜓 ) → ( ( 𝜓 → 𝜓 ) → ( 𝜓 → 𝜓 ) ) ) ) ) → 𝜑 ) → ( ( ( ( 𝜓 → 𝜓 ) → ( ¬ 𝜓 → ¬ ¬ ¬ 𝜑 ) ) → 𝜓 ) → 𝜑 ) ) ) |
5 |
3 4
|
ax-mp |
⊢ ( ( ( ( ( ( 𝜑 → 𝜓 ) → ( ¬ ¬ 𝜑 → 𝜓 ) ) → ¬ ( ( ( ( ( 𝜓 → 𝜓 ) → ( ¬ 𝜓 → ¬ 𝜓 ) ) → 𝜓 ) → 𝜓 ) → ( ( 𝜓 → 𝜓 ) → ( 𝜓 → 𝜓 ) ) ) ) → ( ¬ 𝜑 → ¬ ( ( ( ( ( 𝜓 → 𝜓 ) → ( ¬ 𝜓 → ¬ 𝜓 ) ) → 𝜓 ) → 𝜓 ) → ( ( 𝜓 → 𝜓 ) → ( 𝜓 → 𝜓 ) ) ) ) ) → 𝜑 ) → ( ( ( ( 𝜓 → 𝜓 ) → ( ¬ 𝜓 → ¬ ¬ ¬ 𝜑 ) ) → 𝜓 ) → 𝜑 ) ) |
6 |
|
meredith |
⊢ ( ( ( ( ( ( ( 𝜑 → 𝜓 ) → ( ¬ ¬ 𝜑 → 𝜓 ) ) → ¬ ( ( ( ( ( 𝜓 → 𝜓 ) → ( ¬ 𝜓 → ¬ 𝜓 ) ) → 𝜓 ) → 𝜓 ) → ( ( 𝜓 → 𝜓 ) → ( 𝜓 → 𝜓 ) ) ) ) → ( ¬ 𝜑 → ¬ ( ( ( ( ( 𝜓 → 𝜓 ) → ( ¬ 𝜓 → ¬ 𝜓 ) ) → 𝜓 ) → 𝜓 ) → ( ( 𝜓 → 𝜓 ) → ( 𝜓 → 𝜓 ) ) ) ) ) → 𝜑 ) → ( ( ( ( 𝜓 → 𝜓 ) → ( ¬ 𝜓 → ¬ ¬ ¬ 𝜑 ) ) → 𝜓 ) → 𝜑 ) ) → ( ( ( ( ( ( 𝜓 → 𝜓 ) → ( ¬ 𝜓 → ¬ ¬ ¬ 𝜑 ) ) → 𝜓 ) → 𝜑 ) → ( ( 𝜑 → 𝜓 ) → ( ¬ ¬ 𝜑 → 𝜓 ) ) ) → ( ( ( ( ( ( 𝜓 → 𝜓 ) → ( ¬ 𝜓 → ¬ 𝜓 ) ) → 𝜓 ) → 𝜓 ) → ( ( 𝜓 → 𝜓 ) → ( 𝜓 → 𝜓 ) ) ) → ( ( 𝜑 → 𝜓 ) → ( ¬ ¬ 𝜑 → 𝜓 ) ) ) ) ) |
7 |
5 6
|
ax-mp |
⊢ ( ( ( ( ( ( 𝜓 → 𝜓 ) → ( ¬ 𝜓 → ¬ ¬ ¬ 𝜑 ) ) → 𝜓 ) → 𝜑 ) → ( ( 𝜑 → 𝜓 ) → ( ¬ ¬ 𝜑 → 𝜓 ) ) ) → ( ( ( ( ( ( 𝜓 → 𝜓 ) → ( ¬ 𝜓 → ¬ 𝜓 ) ) → 𝜓 ) → 𝜓 ) → ( ( 𝜓 → 𝜓 ) → ( 𝜓 → 𝜓 ) ) ) → ( ( 𝜑 → 𝜓 ) → ( ¬ ¬ 𝜑 → 𝜓 ) ) ) ) |
8 |
2 7
|
ax-mp |
⊢ ( ( ( ( ( ( 𝜓 → 𝜓 ) → ( ¬ 𝜓 → ¬ 𝜓 ) ) → 𝜓 ) → 𝜓 ) → ( ( 𝜓 → 𝜓 ) → ( 𝜓 → 𝜓 ) ) ) → ( ( 𝜑 → 𝜓 ) → ( ¬ ¬ 𝜑 → 𝜓 ) ) ) |
9 |
1 8
|
ax-mp |
⊢ ( ( 𝜑 → 𝜓 ) → ( ¬ ¬ 𝜑 → 𝜓 ) ) |