Theorem riotaclbBAD

Description: Closure of restricted iota. (Contributed by NM, 15-Sep-2011)

	Ref	Expression
Hypothesis	riotaclb.1	|- A e. _V
Assertion	riotaclbBAD	|- ( E! x e. A ph <-> ( iota_ x e. A ph ) e. A )

Proof

Step	Hyp	Ref	Expression
1		riotaclb.1	|- A e. _V
2		riotaclbgBAD	|- ( A e. _V -> ( E! x e. A ph <-> ( iota_ x e. A ph ) e. A ) )
3	1 2	ax-mp	|- ( E! x e. A ph <-> ( iota_ x e. A ph ) e. A )