Metamath Proof Explorer


Theorem fvprc

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 ) = (/) )

Proof

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 ) = (/) )