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Metamath Proof Explorer
Description: Deduction for proof by contradiction. (Contributed by NM, 26-Jun-1994)
(Proof shortened by Wolf Lammen, 26-May-2013)
|
|
Ref |
Expression |
|
Hypotheses |
pm2.65d.1 |
⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) ) |
|
|
pm2.65d.2 |
⊢ ( 𝜑 → ( 𝜓 → ¬ 𝜒 ) ) |
|
Assertion |
pm2.65d |
⊢ ( 𝜑 → ¬ 𝜓 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
pm2.65d.1 |
⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) ) |
| 2 |
|
pm2.65d.2 |
⊢ ( 𝜑 → ( 𝜓 → ¬ 𝜒 ) ) |
| 3 |
2 1
|
nsyld |
⊢ ( 𝜑 → ( 𝜓 → ¬ 𝜓 ) ) |
| 4 |
3
|
pm2.01d |
⊢ ( 𝜑 → ¬ 𝜓 ) |