Definition df-riota 5488

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 4887. (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 5487	. 2 class (℩𝑥 ∈ 𝐴 𝜑)
5	2	cv 1283	. . . . 5 class 𝑥
6	5, 3	wcel 1433	. . . 4 wff 𝑥 ∈ 𝐴
7	6, 1	wa 102	. . 3 wff (𝑥 ∈ 𝐴 ∧ 𝜑)
8	7, 2	cio 4885	. 2 class (℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))
9	4, 8	wceq 1284	1 wff (℩𝑥 ∈ 𝐴 𝜑) = (℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))

This definition is referenced by:  riotaeqdv  5489  riotabidv  5490  riotaexg  5492  riotav  5493  riotauni  5494  nfriota1  5495  nfriotadxy  5496  cbvriota  5498  riotacl2  5501  riotabidva  5504  riota1  5506  riota2df  5508  snriota  5517  riotaund  5522  bdcriota  10674