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 ∧ ∃! 𝑦 𝐴 𝐹 𝑦 ) → ( 𝐹𝐴 ) = 𝑦 )

Proof

Step Hyp Ref Expression
1 tz6.12c ( ∃! 𝑦 𝐴 𝐹 𝑦 → ( ( 𝐹𝐴 ) = 𝑦𝐴 𝐹 𝑦 ) )
2 1 biimparc ( ( 𝐴 𝐹 𝑦 ∧ ∃! 𝑦 𝐴 𝐹 𝑦 ) → ( 𝐹𝐴 ) = 𝑦 )