Description: Contrapositive law deduction 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 | necon3ad.1 | |- ( ph -> ( ps -> A = B ) ) |
|
| Assertion | necon3ad | |- ( ph -> ( A =/= B -> -. ps ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | necon3ad.1 | |- ( ph -> ( ps -> A = B ) ) |
|
| 2 | neneq | |- ( A =/= B -> -. A = B ) |
|
| 3 | 1 2 | nsyli | |- ( ph -> ( A =/= B -> -. ps ) ) |