Description: Obsolete version of nelb as of 3-Nov-2024. (Contributed by Thierry Arnoux, 20-Nov-2023) (Proof shortened by SN, 23-Jan-2024) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | nelbOLD | |- ( -. A e. B <-> A. x e. B x =/= A ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-ne | |- ( x =/= A <-> -. x = A ) |
|
| 2 | 1 | ralbii | |- ( A. x e. B x =/= A <-> A. x e. B -. x = A ) |
| 3 | ralnex | |- ( A. x e. B -. x = A <-> -. E. x e. B x = A ) |
|
| 4 | 2 3 | bitri | |- ( A. x e. B x =/= A <-> -. E. x e. B x = A ) |
| 5 | risset | |- ( A e. B <-> E. x e. B x = A ) |
|
| 6 | 4 5 | xchbinxr | |- ( A. x e. B x =/= A <-> -. A e. B ) |
| 7 | 6 | bicomi | |- ( -. A e. B <-> A. x e. B x =/= A ) |