Step |
Hyp |
Ref |
Expression |
1 |
|
merco2 |
⊢ ( ( ( 𝜑 → 𝜑 ) → ( ( ⊥ → 𝜑 ) → 𝜑 ) ) → ( ( 𝜑 → 𝜑 ) → ( 𝜑 → ( 𝜑 → 𝜑 ) ) ) ) |
2 |
|
merco2 |
⊢ ( ( ( 𝜒 → 𝜑 ) → ( ( ⊥ → 𝜑 ) → ( 𝜑 → 𝜓 ) ) ) → ( ( ( 𝜑 → 𝜓 ) → 𝜒 ) → ( 𝜓 → ( 𝜃 → 𝜒 ) ) ) ) |
3 |
|
merco2 |
⊢ ( ( ( 𝜓 → ( 𝜃 → 𝜒 ) ) → ( ( ⊥ → 𝜑 ) → ⊥ ) ) → ( ( ⊥ → 𝜓 ) → ( ( ⊥ → 𝜑 ) → ( 𝜑 → 𝜓 ) ) ) ) |
4 |
|
merco2 |
⊢ ( ( ( ( 𝜓 → ( 𝜃 → 𝜒 ) ) → ( ( ⊥ → 𝜑 ) → ⊥ ) ) → ( ( ⊥ → 𝜓 ) → ( ( ⊥ → 𝜑 ) → ( 𝜑 → 𝜓 ) ) ) ) → ( ( ( ( ⊥ → 𝜑 ) → ( 𝜑 → 𝜓 ) ) → ( 𝜓 → ( 𝜃 → 𝜒 ) ) ) → ( ( ⊥ → 𝜑 ) → ( ( ( 𝜑 → 𝜓 ) → 𝜒 ) → ( 𝜓 → ( 𝜃 → 𝜒 ) ) ) ) ) ) |
5 |
3 4
|
ax-mp |
⊢ ( ( ( ( ⊥ → 𝜑 ) → ( 𝜑 → 𝜓 ) ) → ( 𝜓 → ( 𝜃 → 𝜒 ) ) ) → ( ( ⊥ → 𝜑 ) → ( ( ( 𝜑 → 𝜓 ) → 𝜒 ) → ( 𝜓 → ( 𝜃 → 𝜒 ) ) ) ) ) |
6 |
|
merco2 |
⊢ ( ( ( ( ( ⊥ → 𝜑 ) → ( 𝜑 → 𝜓 ) ) → ( 𝜓 → ( 𝜃 → 𝜒 ) ) ) → ( ( ⊥ → 𝜑 ) → ( ( ( 𝜑 → 𝜓 ) → 𝜒 ) → ( 𝜓 → ( 𝜃 → 𝜒 ) ) ) ) ) → ( ( ( ( ( 𝜑 → 𝜓 ) → 𝜒 ) → ( 𝜓 → ( 𝜃 → 𝜒 ) ) ) → ( ( ⊥ → 𝜑 ) → ( 𝜑 → 𝜓 ) ) ) → ( ( ⊥ → 𝜑 ) → ( ( 𝜒 → 𝜑 ) → ( ( ⊥ → 𝜑 ) → ( 𝜑 → 𝜓 ) ) ) ) ) ) |
7 |
5 6
|
ax-mp |
⊢ ( ( ( ( ( 𝜑 → 𝜓 ) → 𝜒 ) → ( 𝜓 → ( 𝜃 → 𝜒 ) ) ) → ( ( ⊥ → 𝜑 ) → ( 𝜑 → 𝜓 ) ) ) → ( ( ⊥ → 𝜑 ) → ( ( 𝜒 → 𝜑 ) → ( ( ⊥ → 𝜑 ) → ( 𝜑 → 𝜓 ) ) ) ) ) |
8 |
|
merco2 |
⊢ ( ( ( ( ( ( 𝜑 → 𝜓 ) → 𝜒 ) → ( 𝜓 → ( 𝜃 → 𝜒 ) ) ) → ( ( ⊥ → 𝜑 ) → ( 𝜑 → 𝜓 ) ) ) → ( ( ⊥ → 𝜑 ) → ( ( 𝜒 → 𝜑 ) → ( ( ⊥ → 𝜑 ) → ( 𝜑 → 𝜓 ) ) ) ) ) → ( ( ( ( 𝜒 → 𝜑 ) → ( ( ⊥ → 𝜑 ) → ( 𝜑 → 𝜓 ) ) ) → ( ( ( 𝜑 → 𝜓 ) → 𝜒 ) → ( 𝜓 → ( 𝜃 → 𝜒 ) ) ) ) → ( ( ( ( 𝜑 → 𝜑 ) → ( ( ⊥ → 𝜑 ) → 𝜑 ) ) → ( ( 𝜑 → 𝜑 ) → ( 𝜑 → ( 𝜑 → 𝜑 ) ) ) ) → ( ( ( ( 𝜑 → 𝜑 ) → ( ( ⊥ → 𝜑 ) → 𝜑 ) ) → ( ( 𝜑 → 𝜑 ) → ( 𝜑 → ( 𝜑 → 𝜑 ) ) ) ) → ( ( ( 𝜑 → 𝜓 ) → 𝜒 ) → ( 𝜓 → ( 𝜃 → 𝜒 ) ) ) ) ) ) ) |
9 |
7 8
|
ax-mp |
⊢ ( ( ( ( 𝜒 → 𝜑 ) → ( ( ⊥ → 𝜑 ) → ( 𝜑 → 𝜓 ) ) ) → ( ( ( 𝜑 → 𝜓 ) → 𝜒 ) → ( 𝜓 → ( 𝜃 → 𝜒 ) ) ) ) → ( ( ( ( 𝜑 → 𝜑 ) → ( ( ⊥ → 𝜑 ) → 𝜑 ) ) → ( ( 𝜑 → 𝜑 ) → ( 𝜑 → ( 𝜑 → 𝜑 ) ) ) ) → ( ( ( ( 𝜑 → 𝜑 ) → ( ( ⊥ → 𝜑 ) → 𝜑 ) ) → ( ( 𝜑 → 𝜑 ) → ( 𝜑 → ( 𝜑 → 𝜑 ) ) ) ) → ( ( ( 𝜑 → 𝜓 ) → 𝜒 ) → ( 𝜓 → ( 𝜃 → 𝜒 ) ) ) ) ) ) |
10 |
2 9
|
ax-mp |
⊢ ( ( ( ( 𝜑 → 𝜑 ) → ( ( ⊥ → 𝜑 ) → 𝜑 ) ) → ( ( 𝜑 → 𝜑 ) → ( 𝜑 → ( 𝜑 → 𝜑 ) ) ) ) → ( ( ( ( 𝜑 → 𝜑 ) → ( ( ⊥ → 𝜑 ) → 𝜑 ) ) → ( ( 𝜑 → 𝜑 ) → ( 𝜑 → ( 𝜑 → 𝜑 ) ) ) ) → ( ( ( 𝜑 → 𝜓 ) → 𝜒 ) → ( 𝜓 → ( 𝜃 → 𝜒 ) ) ) ) ) |
11 |
1 10
|
ax-mp |
⊢ ( ( ( ( 𝜑 → 𝜑 ) → ( ( ⊥ → 𝜑 ) → 𝜑 ) ) → ( ( 𝜑 → 𝜑 ) → ( 𝜑 → ( 𝜑 → 𝜑 ) ) ) ) → ( ( ( 𝜑 → 𝜓 ) → 𝜒 ) → ( 𝜓 → ( 𝜃 → 𝜒 ) ) ) ) |
12 |
1 11
|
ax-mp |
⊢ ( ( ( 𝜑 → 𝜓 ) → 𝜒 ) → ( 𝜓 → ( 𝜃 → 𝜒 ) ) ) |