Metamath Proof Explorer


Theorem tz6.12-2OLD

Description: Obsolete version of tz6.12-2 as of 25-Jan-2026. (Contributed by NM, 30-Apr-2004) (Proof shortened by Mario Carneiro, 31-Aug-2015) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion tz6.12-2OLD
|- ( -. E! x A F x -> ( F ` A ) = (/) )

Proof

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 eqtrid
 |-  ( -. E! x A F x -> ( F ` A ) = (/) )