Definition df-riota 5730

Description: Define restricted description binder. In case there is no unique x such that ( x e. A /\ ph ) holds, it evaluates to the empty set. See also comments for df-iota 5088. (Contributed by NM, 15-Sep-2011.) (Revised by Mario Carneiro, 15-Oct-2016.) (Revised by NM, 2-Sep-2018.)

Assertion

Ref	Expression
df-riota	|- ( iota_ x e. A ph ) = ( iota x ( x e. A /\ ph ) )

Detailed syntax breakdown of Definition df-riota

Step	Hyp	Ref	Expression
1		wph	. . 3 wff ph
2		vx	. . 3 setvar x
3		cA	. . 3 class A
4	1, 2, 3	crio 5729	. 2 class ( iota_ x e. A ph )
5	2	cv 1330	. . . . 5 class x
6	5, 3	wcel 1480	. . . 4 wff x e. A
7	6, 1	wa 103	. . 3 wff ( x e. A /\ ph )
8	7, 2	cio 5086	. 2 class ( iota x ( x e. A /\ ph ) )
9	4, 8	wceq 1331	1 wff ( iota_ x e. A ph ) = ( iota x ( x e. A /\ ph ) )

This definition is referenced by:  riotaeqdv  5731  riotabidv  5732  riotaexg  5734  riotav  5735  riotauni  5736  nfriota1  5737  nfriotadxy  5738  cbvriota  5740  riotacl2  5743  riotabidva  5746  riota1  5748  riota2df  5750  snriota  5759  riotaund  5764  bdcriota  13081