Description: Contrapositive inference for inequality. (Contributed by NM, 2-Apr-2007) (Proof shortened by Andrew Salmon, 25-May-2011) (Proof shortened by Wolf Lammen, 23-Nov-2019)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | necon4ad.1 | |- ( ph -> ( A =/= B -> -. ps ) ) |
|
| Assertion | necon4ad | |- ( ph -> ( ps -> A = B ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | necon4ad.1 | |- ( ph -> ( A =/= B -> -. ps ) ) |
|
| 2 | notnot | |- ( ps -> -. -. ps ) |
|
| 3 | 1 | necon1bd | |- ( ph -> ( -. -. ps -> A = B ) ) |
| 4 | 2 3 | syl5 | |- ( ph -> ( ps -> A = B ) ) |