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