Step |
Hyp |
Ref |
Expression |
1 |
|
merco1 |
⊢ ( ( ( ( ( 𝜒 → 𝜑 ) → ( 𝜏 → ⊥ ) ) → 𝜑 ) → ( 𝜑 → 𝜓 ) ) → ( ( ( 𝜑 → 𝜓 ) → 𝜒 ) → ( 𝜏 → 𝜒 ) ) ) |
2 |
|
merco1lem2 |
⊢ ( ( ( ( ( ( 𝜒 → 𝜑 ) → ( 𝜏 → ⊥ ) ) → 𝜑 ) → ( 𝜑 → 𝜓 ) ) → ( ( ( 𝜑 → 𝜓 ) → 𝜒 ) → ( 𝜏 → 𝜒 ) ) ) → ( ( ( ( 𝜑 → 𝜓 ) → ( 𝜃 → ⊥ ) ) → ( ( ( ( 𝜒 → 𝜑 ) → ( 𝜏 → ⊥ ) ) → 𝜑 ) → ⊥ ) ) → ( ( ( 𝜑 → 𝜓 ) → 𝜒 ) → ( 𝜏 → 𝜒 ) ) ) ) |
3 |
1 2
|
ax-mp |
⊢ ( ( ( ( 𝜑 → 𝜓 ) → ( 𝜃 → ⊥ ) ) → ( ( ( ( 𝜒 → 𝜑 ) → ( 𝜏 → ⊥ ) ) → 𝜑 ) → ⊥ ) ) → ( ( ( 𝜑 → 𝜓 ) → 𝜒 ) → ( 𝜏 → 𝜒 ) ) ) |
4 |
|
merco1 |
⊢ ( ( ( ( ( 𝜑 → 𝜓 ) → ( 𝜃 → ⊥ ) ) → ( ( ( ( 𝜒 → 𝜑 ) → ( 𝜏 → ⊥ ) ) → 𝜑 ) → ⊥ ) ) → ( ( ( 𝜑 → 𝜓 ) → 𝜒 ) → ( 𝜏 → 𝜒 ) ) ) → ( ( ( ( ( 𝜑 → 𝜓 ) → 𝜒 ) → ( 𝜏 → 𝜒 ) ) → 𝜑 ) → ( 𝜃 → 𝜑 ) ) ) |
5 |
3 4
|
ax-mp |
⊢ ( ( ( ( ( 𝜑 → 𝜓 ) → 𝜒 ) → ( 𝜏 → 𝜒 ) ) → 𝜑 ) → ( 𝜃 → 𝜑 ) ) |