Step |
Hyp |
Ref |
Expression |
1 |
|
luk-1 |
⊢ ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( ( ( 𝜓 → 𝜒 ) → 𝜒 ) → ( 𝜑 → 𝜒 ) ) ) |
2 |
|
luklem5 |
⊢ ( 𝜓 → ( ( 𝜓 → 𝜒 ) → 𝜓 ) ) |
3 |
|
luk-1 |
⊢ ( ( ( 𝜓 → 𝜒 ) → 𝜓 ) → ( ( 𝜓 → 𝜒 ) → ( ( 𝜓 → 𝜒 ) → 𝜒 ) ) ) |
4 |
2 3
|
luklem1 |
⊢ ( 𝜓 → ( ( 𝜓 → 𝜒 ) → ( ( 𝜓 → 𝜒 ) → 𝜒 ) ) ) |
5 |
|
luklem6 |
⊢ ( ( ( 𝜓 → 𝜒 ) → ( ( 𝜓 → 𝜒 ) → 𝜒 ) ) → ( ( 𝜓 → 𝜒 ) → 𝜒 ) ) |
6 |
4 5
|
luklem1 |
⊢ ( 𝜓 → ( ( 𝜓 → 𝜒 ) → 𝜒 ) ) |
7 |
|
luk-1 |
⊢ ( ( 𝜓 → ( ( 𝜓 → 𝜒 ) → 𝜒 ) ) → ( ( ( ( 𝜓 → 𝜒 ) → 𝜒 ) → ( 𝜑 → 𝜒 ) ) → ( 𝜓 → ( 𝜑 → 𝜒 ) ) ) ) |
8 |
6 7
|
ax-mp |
⊢ ( ( ( ( 𝜓 → 𝜒 ) → 𝜒 ) → ( 𝜑 → 𝜒 ) ) → ( 𝜓 → ( 𝜑 → 𝜒 ) ) ) |
9 |
1 8
|
luklem1 |
⊢ ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( 𝜓 → ( 𝜑 → 𝜒 ) ) ) |