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	$$⊢\left(AFy\wedge \exists !yAFy\right)\to F\left(A\right)=y$$

Proof

Step	Hyp	Ref	Expression
1		tz6.12c	$$⊢\exists !yAFy\to \left(F\left(A\right)=y\leftrightarrow AFy\right)$$
2	1	biimparc	$$⊢\left(AFy\wedge \exists !yAFy\right)\to F\left(A\right)=y$$