Theorem tz6.12-1OLD

Description: Obsolete version of tz6.12-1 as of 23-Dec-2024. (Contributed by NM, 30-Apr-2004) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	tz6.12-1OLD	$$⊢\left(AFy\wedge \exists !yAFy\right)\to F\left(A\right)=y$$

Proof

Step	Hyp	Ref	Expression
1		df-fv	$$⊢F\left(A\right)=\left(\iota y|AFy\right)$$
2		iota1	$$⊢\exists !yAFy\to \left(AFy\leftrightarrow \left(\iota y|AFy\right)=y\right)$$
3	2	biimpac	$$⊢\left(AFy\wedge \exists !yAFy\right)\to \left(\iota y|AFy\right)=y$$
4	1 3	eqtrid	$$⊢\left(AFy\wedge \exists !yAFy\right)\to F\left(A\right)=y$$