Step |
Hyp |
Ref |
Expression |
1 |
|
tbw-ax3 |
⊢ ( ( ( 𝜑 → ⊥ ) → 𝜑 ) → 𝜑 ) |
2 |
|
tbw-ax2 |
⊢ ( ( ( ( 𝜑 → ⊥ ) → 𝜑 ) → 𝜑 ) → ( ( ( ( ( 𝜑 → ⊥ ) → 𝜑 ) → 𝜑 ) → 𝜓 ) → ( ( ( 𝜑 → ⊥ ) → 𝜑 ) → 𝜑 ) ) ) |
3 |
|
tbw-ax1 |
⊢ ( ( ( ( ( ( 𝜑 → ⊥ ) → 𝜑 ) → 𝜑 ) → 𝜓 ) → ( ( ( 𝜑 → ⊥ ) → 𝜑 ) → 𝜑 ) ) → ( ( ( ( ( 𝜑 → ⊥ ) → 𝜑 ) → 𝜑 ) → 𝜓 ) → ( ( ( ( ( 𝜑 → ⊥ ) → 𝜑 ) → 𝜑 ) → 𝜓 ) → 𝜓 ) ) ) |
4 |
2 3
|
tbwsyl |
⊢ ( ( ( ( 𝜑 → ⊥ ) → 𝜑 ) → 𝜑 ) → ( ( ( ( ( 𝜑 → ⊥ ) → 𝜑 ) → 𝜑 ) → 𝜓 ) → ( ( ( ( ( 𝜑 → ⊥ ) → 𝜑 ) → 𝜑 ) → 𝜓 ) → 𝜓 ) ) ) |
5 |
1 4
|
ax-mp |
⊢ ( ( ( ( ( 𝜑 → ⊥ ) → 𝜑 ) → 𝜑 ) → 𝜓 ) → ( ( ( ( ( 𝜑 → ⊥ ) → 𝜑 ) → 𝜑 ) → 𝜓 ) → 𝜓 ) ) |
6 |
|
tbw-ax1 |
⊢ ( ( ( ( ( ( 𝜑 → ⊥ ) → 𝜑 ) → 𝜑 ) → 𝜓 ) → ( ( ( ( ( 𝜑 → ⊥ ) → 𝜑 ) → 𝜑 ) → 𝜓 ) → 𝜓 ) ) → ( ( ( ( ( ( ( 𝜑 → ⊥ ) → 𝜑 ) → 𝜑 ) → 𝜓 ) → 𝜓 ) → 𝜓 ) → ( ( ( ( ( 𝜑 → ⊥ ) → 𝜑 ) → 𝜑 ) → 𝜓 ) → 𝜓 ) ) ) |
7 |
|
tbw-ax3 |
⊢ ( ( ( ( ( ( ( ( 𝜑 → ⊥ ) → 𝜑 ) → 𝜑 ) → 𝜓 ) → 𝜓 ) → 𝜓 ) → ( ( ( ( ( 𝜑 → ⊥ ) → 𝜑 ) → 𝜑 ) → 𝜓 ) → 𝜓 ) ) → ( ( ( ( ( 𝜑 → ⊥ ) → 𝜑 ) → 𝜑 ) → 𝜓 ) → 𝜓 ) ) |
8 |
6 7
|
tbwsyl |
⊢ ( ( ( ( ( ( 𝜑 → ⊥ ) → 𝜑 ) → 𝜑 ) → 𝜓 ) → ( ( ( ( ( 𝜑 → ⊥ ) → 𝜑 ) → 𝜑 ) → 𝜓 ) → 𝜓 ) ) → ( ( ( ( ( 𝜑 → ⊥ ) → 𝜑 ) → 𝜑 ) → 𝜓 ) → 𝜓 ) ) |
9 |
5 8
|
ax-mp |
⊢ ( ( ( ( ( 𝜑 → ⊥ ) → 𝜑 ) → 𝜑 ) → 𝜓 ) → 𝜓 ) |