Description: A class is nonempty if and only if it has at least one element. Proposition 5.17(1) of TakeutiZaring p. 20. (Contributed by NM, 29-Sep-2006) Avoid ax-11 , ax-12 . (Revised by Gino Giotto, 28-Jun-2024)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | n0 | |- ( A =/= (/) <-> E. x x e. A ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-ne | |- ( A =/= (/) <-> -. A = (/) ) |
|
| 2 | neq0 | |- ( -. A = (/) <-> E. x x e. A ) |
|
| 3 | 1 2 | bitri | |- ( A =/= (/) <-> E. x x e. A ) |