Description: Contrapositive inference for inequality. (Contributed by NM, 18-Mar-2007) (Proof shortened by Andrew Salmon, 25-May-2011) (Proof shortened by Wolf Lammen, 22-Nov-2019)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | necon1bi.1 | |- ( A =/= B -> ph ) |
|
| Assertion | necon1bi | |- ( -. ph -> A = B ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | necon1bi.1 | |- ( A =/= B -> ph ) |
|
| 2 | df-ne | |- ( A =/= B <-> -. A = B ) |
|
| 3 | 2 1 | sylbir | |- ( -. A = B -> ph ) |
| 4 | 3 | con1i | |- ( -. ph -> A = B ) |