Description: Contrapositive inference for inequality. (Contributed by NM, 23-May-2007) (Proof shortened by Andrew Salmon, 25-May-2011) (Proof shortened by Wolf Lammen, 28-Oct-2024)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | necon3ai.1 | |- ( ph -> A = B ) |
|
| Assertion | necon3ai | |- ( A =/= B -> -. ph ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | necon3ai.1 | |- ( ph -> A = B ) |
|
| 2 | neneq | |- ( A =/= B -> -. A = B ) |
|
| 3 | 2 1 | nsyl | |- ( A =/= B -> -. ph ) |