Step |
Hyp |
Ref |
Expression |
1 |
|
merco1lem5 |
⊢ ( ( ( ( ( ( ( 𝜑 → 𝜓 ) → ⊥ ) → ( 𝜒 → ⊥ ) ) → ⊥ ) → ⊥ ) → ⊥ ) → ( ( ( ( 𝜑 → 𝜓 ) → ⊥ ) → ( 𝜒 → ⊥ ) ) → ⊥ ) ) |
2 |
|
merco1lem3 |
⊢ ( ( ( ( ( ( ( ( 𝜑 → 𝜓 ) → ⊥ ) → ( 𝜒 → ⊥ ) ) → ⊥ ) → ⊥ ) → ⊥ ) → ( ( ( ( 𝜑 → 𝜓 ) → ⊥ ) → ( 𝜒 → ⊥ ) ) → ⊥ ) ) → ( ( ( ( 𝜑 → 𝜓 ) → ⊥ ) → ( 𝜒 → ⊥ ) ) → ( ( ( ( ( 𝜑 → 𝜓 ) → ⊥ ) → ( 𝜒 → ⊥ ) ) → ⊥ ) → ⊥ ) ) ) |
3 |
1 2
|
ax-mp |
⊢ ( ( ( ( 𝜑 → 𝜓 ) → ⊥ ) → ( 𝜒 → ⊥ ) ) → ( ( ( ( ( 𝜑 → 𝜓 ) → ⊥ ) → ( 𝜒 → ⊥ ) ) → ⊥ ) → ⊥ ) ) |
4 |
|
merco1lem5 |
⊢ ( ( ( ( ( 𝜑 → 𝜓 ) → ⊥ ) → ( 𝜒 → ⊥ ) ) → ( ( ( ( ( 𝜑 → 𝜓 ) → ⊥ ) → ( 𝜒 → ⊥ ) ) → ⊥ ) → ⊥ ) ) → ( ( 𝜑 → 𝜓 ) → ( ( ( ( ( 𝜑 → 𝜓 ) → ⊥ ) → ( 𝜒 → ⊥ ) ) → ⊥ ) → ⊥ ) ) ) |
5 |
3 4
|
ax-mp |
⊢ ( ( 𝜑 → 𝜓 ) → ( ( ( ( ( 𝜑 → 𝜓 ) → ⊥ ) → ( 𝜒 → ⊥ ) ) → ⊥ ) → ⊥ ) ) |
6 |
|
merco1lem3 |
⊢ ( ( ( 𝜑 → 𝜓 ) → ( ( ( ( ( 𝜑 → 𝜓 ) → ⊥ ) → ( 𝜒 → ⊥ ) ) → ⊥ ) → ⊥ ) ) → ( ( ( ( ( 𝜑 → 𝜓 ) → ⊥ ) → ( 𝜒 → ⊥ ) ) → ⊥ ) → 𝜑 ) ) |
7 |
5 6
|
ax-mp |
⊢ ( ( ( ( ( 𝜑 → 𝜓 ) → ⊥ ) → ( 𝜒 → ⊥ ) ) → ⊥ ) → 𝜑 ) |
8 |
|
merco1 |
⊢ ( ( ( ( ( ( 𝜑 → 𝜓 ) → ⊥ ) → ( 𝜒 → ⊥ ) ) → ⊥ ) → 𝜑 ) → ( ( 𝜑 → ( 𝜑 → 𝜓 ) ) → ( 𝜒 → ( 𝜑 → 𝜓 ) ) ) ) |
9 |
7 8
|
ax-mp |
⊢ ( ( 𝜑 → ( 𝜑 → 𝜓 ) ) → ( 𝜒 → ( 𝜑 → 𝜓 ) ) ) |