Definition df-riota 5468

Description: Define restricted description binder. In case there is no unique 𝑥 such that (𝑥 ∈ 𝐴 ∧ 𝜑) holds, it evaluates to the empty set. See also comments for df-iota 4867. (Contributed by NM, 15-Sep-2011.) (Revised by Mario Carneiro, 15-Oct-2016.) (Revised by NM, 2-Sep-2018.)

Assertion

Ref	Expression
df-riota	⊢ (℩𝑥 ∈ 𝐴 𝜑) = (℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))

Detailed syntax breakdown of Definition df-riota

Step	Hyp	Ref	Expression
1		wph	. . 3 wff 𝜑
2		vx	. . 3 setvar 𝑥
3		cA	. . 3 class 𝐴
4	1, 2, 3	crio 5467	. 2 class (℩𝑥 ∈ 𝐴 𝜑)
5	2	cv 1242	. . . . 5 class 𝑥
6	5, 3	wcel 1393	. . . 4 wff 𝑥 ∈ 𝐴
7	6, 1	wa 97	. . 3 wff (𝑥 ∈ 𝐴 ∧ 𝜑)
8	7, 2	cio 4865	. 2 class (℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))
9	4, 8	wceq 1243	1 wff (℩𝑥 ∈ 𝐴 𝜑) = (℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))

This definition is referenced by:  riotaeqdv  5469  riotabidv  5470  riotaexg  5472  riotav  5473  riotauni  5474  nfriota1  5475  nfriotadxy  5476  cbvriota  5478  riotacl2  5481  riotabidva  5484  riota1  5486  riota2df  5488  snriota  5497  riotaund  5502  bdcriota  10003