This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.
Metamath Proof Explorer
Description: Deduction based on reductio ad absurdum. See pm2.18 . (Contributed by Mario Carneiro, 9-Feb-2017)
|
|
Ref |
Expression |
|
Hypothesis |
pm2.18da.1 |
⊢ ( ( 𝜑 ∧ ¬ 𝜓 ) → 𝜓 ) |
|
Assertion |
pm2.18da |
⊢ ( 𝜑 → 𝜓 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
pm2.18da.1 |
⊢ ( ( 𝜑 ∧ ¬ 𝜓 ) → 𝜓 ) |
| 2 |
1
|
ex |
⊢ ( 𝜑 → ( ¬ 𝜓 → 𝜓 ) ) |
| 3 |
2
|
pm2.18d |
⊢ ( 𝜑 → 𝜓 ) |