Definition df-riota 6031

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 5335. (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 6030	. 2 class (℩𝑥 ∈ 𝐴 𝜑)
5	2	cv 1401	. . . . 5 class 𝑥
6	5, 3	wcel 2209	. . . 4 wff 𝑥 ∈ 𝐴
7	6, 1	wa 104	. . 3 wff (𝑥 ∈ 𝐴 ∧ 𝜑)
8	7, 2	cio 5333	. 2 class (℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))
9	4, 8	wceq 1402	1 wff (℩𝑥 ∈ 𝐴 𝜑) = (℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))

This definition is referenced by:  riotaeqdv  6032  riotabidv  6033  riotaexg  6035  iotaexel  6036  riotav  6037  riotauni  6038  nfriota1  6039  nfriotadxy  6040  cbvriotavw  6042  cbvriota  6043  riotacl2  6046  riotabidva  6049  riota1  6051  riota2df  6053  snriota  6063  riotaund  6068  grpidvalg  13673  fn0g  13675  ismgmid  13677  oppr1g  14364  bdcriota  16826