Description: If it is not the case that two classes are equal, then they are unequal. Converse of neneqd . One-way deduction form of df-ne . (Contributed by David Moews, 28-Feb-2017) Allow a shortening of necon3bi . (Revised by Wolf Lammen, 22-Nov-2019)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | neqned.1 | |- ( ph -> -. A = B ) |
|
| Assertion | neqned | |- ( ph -> A =/= B ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | neqned.1 | |- ( ph -> -. A = B ) |
|
| 2 | df-ne | |- ( A =/= B <-> -. A = B ) |
|
| 3 | 1 2 | sylibr | |- ( ph -> A =/= B ) |