Definition df-riota 5809

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 5160. (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 5808	. 2 class (℩𝑥 ∈ 𝐴 𝜑)
5	2	cv 1347	. . . . 5 class 𝑥
6	5, 3	wcel 2141	. . . 4 wff 𝑥 ∈ 𝐴
7	6, 1	wa 103	. . 3 wff (𝑥 ∈ 𝐴 ∧ 𝜑)
8	7, 2	cio 5158	. 2 class (℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))
9	4, 8	wceq 1348	1 wff (℩𝑥 ∈ 𝐴 𝜑) = (℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))

This definition is referenced by:  riotaeqdv  5810  riotabidv  5811  riotaexg  5813  riotav  5814  riotauni  5815  nfriota1  5816  nfriotadxy  5817  cbvriota  5819  riotacl2  5822  riotabidva  5825  riota1  5827  riota2df  5829  snriota  5838  riotaund  5843  grpidvalg  12627  fn0g  12629  ismgmid  12631  bdcriota  13918