Step |
Hyp |
Ref |
Expression |
1 |
|
merlem4 |
⊢ ( ( 𝜓 → 𝜒 ) → ( ( ( 𝜓 → 𝜒 ) → 𝜃 ) → ( ( ( 𝜒 → 𝜏 ) → ( ¬ 𝜃 → ¬ 𝜓 ) ) → 𝜃 ) ) ) |
2 |
|
merlem6 |
⊢ ( ( ( ( 𝜒 → 𝜏 ) → ( ¬ 𝜃 → ¬ 𝜓 ) ) → 𝜃 ) → ( ( ( ( ( 𝜓 → 𝜒 ) → 𝜃 ) → ( ( ( 𝜒 → 𝜏 ) → ( ¬ 𝜃 → ¬ 𝜓 ) ) → 𝜃 ) ) → ¬ 𝜑 ) → ( ¬ 𝜒 → ¬ 𝜑 ) ) ) |
3 |
|
meredith |
⊢ ( ( ( ( ( 𝜒 → 𝜏 ) → ( ¬ 𝜃 → ¬ 𝜓 ) ) → 𝜃 ) → ( ( ( ( ( 𝜓 → 𝜒 ) → 𝜃 ) → ( ( ( 𝜒 → 𝜏 ) → ( ¬ 𝜃 → ¬ 𝜓 ) ) → 𝜃 ) ) → ¬ 𝜑 ) → ( ¬ 𝜒 → ¬ 𝜑 ) ) ) → ( ( ( ( ( ( ( 𝜓 → 𝜒 ) → 𝜃 ) → ( ( ( 𝜒 → 𝜏 ) → ( ¬ 𝜃 → ¬ 𝜓 ) ) → 𝜃 ) ) → ¬ 𝜑 ) → ( ¬ 𝜒 → ¬ 𝜑 ) ) → 𝜒 ) → ( 𝜓 → 𝜒 ) ) ) |
4 |
2 3
|
ax-mp |
⊢ ( ( ( ( ( ( ( 𝜓 → 𝜒 ) → 𝜃 ) → ( ( ( 𝜒 → 𝜏 ) → ( ¬ 𝜃 → ¬ 𝜓 ) ) → 𝜃 ) ) → ¬ 𝜑 ) → ( ¬ 𝜒 → ¬ 𝜑 ) ) → 𝜒 ) → ( 𝜓 → 𝜒 ) ) |
5 |
|
meredith |
⊢ ( ( ( ( ( ( ( ( 𝜓 → 𝜒 ) → 𝜃 ) → ( ( ( 𝜒 → 𝜏 ) → ( ¬ 𝜃 → ¬ 𝜓 ) ) → 𝜃 ) ) → ¬ 𝜑 ) → ( ¬ 𝜒 → ¬ 𝜑 ) ) → 𝜒 ) → ( 𝜓 → 𝜒 ) ) → ( ( ( 𝜓 → 𝜒 ) → ( ( ( 𝜓 → 𝜒 ) → 𝜃 ) → ( ( ( 𝜒 → 𝜏 ) → ( ¬ 𝜃 → ¬ 𝜓 ) ) → 𝜃 ) ) ) → ( 𝜑 → ( ( ( 𝜓 → 𝜒 ) → 𝜃 ) → ( ( ( 𝜒 → 𝜏 ) → ( ¬ 𝜃 → ¬ 𝜓 ) ) → 𝜃 ) ) ) ) ) |
6 |
4 5
|
ax-mp |
⊢ ( ( ( 𝜓 → 𝜒 ) → ( ( ( 𝜓 → 𝜒 ) → 𝜃 ) → ( ( ( 𝜒 → 𝜏 ) → ( ¬ 𝜃 → ¬ 𝜓 ) ) → 𝜃 ) ) ) → ( 𝜑 → ( ( ( 𝜓 → 𝜒 ) → 𝜃 ) → ( ( ( 𝜒 → 𝜏 ) → ( ¬ 𝜃 → ¬ 𝜓 ) ) → 𝜃 ) ) ) ) |
7 |
1 6
|
ax-mp |
⊢ ( 𝜑 → ( ( ( 𝜓 → 𝜒 ) → 𝜃 ) → ( ( ( 𝜒 → 𝜏 ) → ( ¬ 𝜃 → ¬ 𝜓 ) ) → 𝜃 ) ) ) |