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Metamath Proof Explorer
Description: Inference for proof by contradiction. (Contributed by NM, 18-May-1994)
(Proof shortened by Wolf Lammen, 11-Sep-2013)
|
|
Ref |
Expression |
|
Hypotheses |
pm2.65i.1 |
|- ( ph -> ps ) |
|
|
pm2.65i.2 |
|- ( ph -> -. ps ) |
|
Assertion |
pm2.65i |
|- -. ph |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
pm2.65i.1 |
|- ( ph -> ps ) |
| 2 |
|
pm2.65i.2 |
|- ( ph -> -. ps ) |
| 3 |
2
|
con2i |
|- ( ps -> -. ph ) |
| 4 |
1
|
con3i |
|- ( -. ps -> -. ph ) |
| 5 |
3 4
|
pm2.61i |
|- -. ph |