Description: A function's value at a proper class is the empty set. See fvprcALT for a proof that uses ax-pow instead of ax-pr . (Contributed by NM, 20-May-1998) Avoid ax-pow . (Revised by BTernaryTau, 3-Aug-2024) (Proof shortened by BTernaryTau, 3-Dec-2024)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | fvprc | |- ( -. A e. _V -> ( F ` A ) = (/) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | brprcneu | |- ( -. A e. _V -> -. E! x A F x ) |
|
| 2 | tz6.12-2 | |- ( -. E! x A F x -> ( F ` A ) = (/) ) |
|
| 3 | 1 2 | syl | |- ( -. A e. _V -> ( F ` A ) = (/) ) |