Description: Function value when F is not a function. Theorem 6.12(2) of TakeutiZaring p. 27. (Contributed by NM, 30-Apr-2004) (Proof shortened by Mario Carneiro, 31-Aug-2015)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | tz6.12-2 | |- ( -. E! x A F x -> ( F ` A ) = (/) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-fv | |- ( F ` A ) = ( iota x A F x ) |
|
| 2 | iotanul | |- ( -. E! x A F x -> ( iota x A F x ) = (/) ) |
|
| 3 | 1 2 | syl5eq | |- ( -. E! x A F x -> ( F ` A ) = (/) ) |