Theorem iota0ndef

Description: Example for an undefined iota being the empty set, i.e., A. y y e. x is a wff not satisfied by a (unique) value x (there is no set, and therefore certainly no unique set, which contains every set). (Contributed by AV, 24-Aug-2022)

	Ref	Expression
Assertion	iota0ndef	|- ( iota x A. y y e. x ) = (/)

Proof

Step	Hyp	Ref	Expression
1		nalset	|- -. E. x A. y y e. x
2	1	intnanr	|- -. ( E. x A. y y e. x /\ E* x A. y y e. x )
3		df-eu	|- ( E! x A. y y e. x <-> ( E. x A. y y e. x /\ E* x A. y y e. x ) )
4	2 3	mtbir	|- -. E! x A. y y e. x
5		iotanul	|- ( -. E! x A. y y e. x -> ( iota x A. y y e. x ) = (/) )
6	4 5	ax-mp	|- ( iota x A. y y e. x ) = (/)