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Metamath Proof Explorer

Theorem tz6.12-1

Description: Function value. Theorem 6.12(1) of TakeutiZaring p. 27. (Contributed by NM, 30-Apr-2004) (Proof shortened by SN, 23-Dec-2024)

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

Proof

Step Hyp Ref Expression
1 tz6.12c 
 |-  ( E! y A F y -> ( ( F ` A ) = y <-> A F y ) )
2 1 biimparc 
 |-  ( ( A F y /\ E! y A F y ) -> ( F ` A ) = y )