Description: Contrapositive inference for inequality. (Contributed by NM, 18-Mar-2007)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | necon1i.1 | |- ( A =/= B -> C = D ) |
|
| Assertion | necon1i | |- ( C =/= D -> A = B ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | necon1i.1 | |- ( A =/= B -> C = D ) |
|
| 2 | df-ne | |- ( A =/= B <-> -. A = B ) |
|
| 3 | 2 1 | sylbir | |- ( -. A = B -> C = D ) |
| 4 | 3 | necon1ai | |- ( C =/= D -> A = B ) |