Step |
Hyp |
Ref |
Expression |
1 |
|
merlem5 |
⊢ ( ( 𝜑 → ¬ ( ¬ 𝜑 → 𝜑 ) ) → ( ¬ ¬ 𝜑 → ¬ ( ¬ 𝜑 → 𝜑 ) ) ) |
2 |
|
merlem4 |
⊢ ( ( ( 𝜑 → ¬ ( ¬ 𝜑 → 𝜑 ) ) → ( ¬ ¬ 𝜑 → ¬ ( ¬ 𝜑 → 𝜑 ) ) ) → ( ( ( ( 𝜑 → ¬ ( ¬ 𝜑 → 𝜑 ) ) → ( ¬ ¬ 𝜑 → ¬ ( ¬ 𝜑 → 𝜑 ) ) ) → ¬ 𝜑 ) → ( ( ( ( 𝜑 → ¬ ( ¬ 𝜑 → 𝜑 ) ) → ( ¬ ¬ 𝜑 → ¬ ( ¬ 𝜑 → 𝜑 ) ) ) → ¬ 𝜑 ) → ¬ 𝜑 ) ) ) |
3 |
1 2
|
ax-mp |
⊢ ( ( ( ( 𝜑 → ¬ ( ¬ 𝜑 → 𝜑 ) ) → ( ¬ ¬ 𝜑 → ¬ ( ¬ 𝜑 → 𝜑 ) ) ) → ¬ 𝜑 ) → ( ( ( ( 𝜑 → ¬ ( ¬ 𝜑 → 𝜑 ) ) → ( ¬ ¬ 𝜑 → ¬ ( ¬ 𝜑 → 𝜑 ) ) ) → ¬ 𝜑 ) → ¬ 𝜑 ) ) |
4 |
|
merlem11 |
⊢ ( ( ( ( ( 𝜑 → ¬ ( ¬ 𝜑 → 𝜑 ) ) → ( ¬ ¬ 𝜑 → ¬ ( ¬ 𝜑 → 𝜑 ) ) ) → ¬ 𝜑 ) → ( ( ( ( 𝜑 → ¬ ( ¬ 𝜑 → 𝜑 ) ) → ( ¬ ¬ 𝜑 → ¬ ( ¬ 𝜑 → 𝜑 ) ) ) → ¬ 𝜑 ) → ¬ 𝜑 ) ) → ( ( ( ( 𝜑 → ¬ ( ¬ 𝜑 → 𝜑 ) ) → ( ¬ ¬ 𝜑 → ¬ ( ¬ 𝜑 → 𝜑 ) ) ) → ¬ 𝜑 ) → ¬ 𝜑 ) ) |
5 |
3 4
|
ax-mp |
⊢ ( ( ( ( 𝜑 → ¬ ( ¬ 𝜑 → 𝜑 ) ) → ( ¬ ¬ 𝜑 → ¬ ( ¬ 𝜑 → 𝜑 ) ) ) → ¬ 𝜑 ) → ¬ 𝜑 ) |
6 |
|
meredith |
⊢ ( ( ( ( ( 𝜑 → ¬ ( ¬ 𝜑 → 𝜑 ) ) → ( ¬ ¬ 𝜑 → ¬ ( ¬ 𝜑 → 𝜑 ) ) ) → ¬ 𝜑 ) → ¬ 𝜑 ) → ( ( ¬ 𝜑 → 𝜑 ) → ( ( ¬ 𝜑 → 𝜑 ) → 𝜑 ) ) ) |
7 |
5 6
|
ax-mp |
⊢ ( ( ¬ 𝜑 → 𝜑 ) → ( ( ¬ 𝜑 → 𝜑 ) → 𝜑 ) ) |
8 |
|
merlem11 |
⊢ ( ( ( ¬ 𝜑 → 𝜑 ) → ( ( ¬ 𝜑 → 𝜑 ) → 𝜑 ) ) → ( ( ¬ 𝜑 → 𝜑 ) → 𝜑 ) ) |
9 |
7 8
|
ax-mp |
⊢ ( ( ¬ 𝜑 → 𝜑 ) → 𝜑 ) |