Theorem tz6.12-2

Description: Function value when F is not a function. Theorem 6.12(2) of TakeutiZaring p. 27. (Contributed by NM, 30-Apr-2004) (Proof shortened by Mario Carneiro, 31-Aug-2015)

	Ref	Expression
Assertion	tz6.12-2	$$⊢\neg \exists !xAFx\to F\left(A\right)=\varnothing$$

Proof

Step	Hyp	Ref	Expression
1		df-fv	$$⊢F\left(A\right)=\left(\iota x|AFx\right)$$
2		iotanul	$$⊢\neg \exists !xAFx\to \left(\iota x|AFx\right)=\varnothing$$
3	1 2	eqtrid	$$⊢\neg \exists !xAFx\to F\left(A\right)=\varnothing$$