Metamath Proof Explorer
Description: If a wff and its negation are provable, then falsum is provable.
(Contributed by Mario Carneiro, 9-Feb-2017)
|
|
Ref |
Expression |
|
Hypotheses |
pm2.21fal.1 |
|- ( ph -> ps ) |
|
|
pm2.21fal.2 |
|- ( ph -> -. ps ) |
|
Assertion |
pm2.21fal |
|- ( ph -> F. ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
pm2.21fal.1 |
|- ( ph -> ps ) |
2 |
|
pm2.21fal.2 |
|- ( ph -> -. ps ) |
3 |
1 2
|
pm2.21dd |
|- ( ph -> F. ) |