Description: Contrapositive inference for inequality. (Contributed by NM, 17-Mar-2007) (Proof shortened by Andrew Salmon, 25-May-2011) (Proof shortened by Wolf Lammen, 24-Nov-2019)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | necon4i.1 | |- ( A =/= B -> C =/= D ) |
|
| Assertion | necon4i | |- ( C = D -> A = B ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | necon4i.1 | |- ( A =/= B -> C =/= D ) |
|
| 2 | 1 | neneqd | |- ( A =/= B -> -. C = D ) |
| 3 | 2 | necon4ai | |- ( C = D -> A = B ) |