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 ) → ( 𝐹 ‘ 𝐴 ) = 𝑦 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tz6.12c | ⊢ ( ∃! 𝑦 𝐴 𝐹 𝑦 → ( ( 𝐹 ‘ 𝐴 ) = 𝑦 ↔ 𝐴 𝐹 𝑦 ) ) | |
2 | 1 | biimparc | ⊢ ( ( 𝐴 𝐹 𝑦 ∧ ∃! 𝑦 𝐴 𝐹 𝑦 ) → ( 𝐹 ‘ 𝐴 ) = 𝑦 ) |