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Metamath Proof Explorer
Description: Deduction based on reductio ad absurdum. (Contributed by NM, 18-Aug-1993) (Proof shortened by Wolf Lammen, 5-Mar-2013)
|
|
Ref |
Expression |
|
Hypothesis |
pm2.01d.1 |
⊢ ( 𝜑 → ( 𝜓 → ¬ 𝜓 ) ) |
|
Assertion |
pm2.01d |
⊢ ( 𝜑 → ¬ 𝜓 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
pm2.01d.1 |
⊢ ( 𝜑 → ( 𝜓 → ¬ 𝜓 ) ) |
| 2 |
|
id |
⊢ ( ¬ 𝜓 → ¬ 𝜓 ) |
| 3 |
1 2
|
pm2.61d1 |
⊢ ( 𝜑 → ¬ 𝜓 ) |