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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 ∧ ∃! y A F y → F ⁡ A = y

Proof

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