Metamath Proof Explorer


Theorem tz6.12-1OLD

Description: Obsolete version of tz6.12-1 as of 23-Dec-2024. (Contributed by NM, 30-Apr-2004) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion tz6.12-1OLD
|- ( ( A F y /\ E! y A F y ) -> ( F ` A ) = y )

Proof

Step Hyp Ref Expression
1 df-fv
 |-  ( F ` A ) = ( iota y A F y )
2 iota1
 |-  ( E! y A F y -> ( A F y <-> ( iota y A F y ) = y ) )
3 2 biimpac
 |-  ( ( A F y /\ E! y A F y ) -> ( iota y A F y ) = y )
4 1 3 eqtrid
 |-  ( ( A F y /\ E! y A F y ) -> ( F ` A ) = y )