Definition df-riota 5830

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 5178. (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 5829	. 2 class (℩𝑥 ∈ 𝐴 𝜑)
5	2	cv 1352	. . . . 5 class 𝑥
6	5, 3	wcel 2148	. . . 4 wff 𝑥 ∈ 𝐴
7	6, 1	wa 104	. . 3 wff (𝑥 ∈ 𝐴 ∧ 𝜑)
8	7, 2	cio 5176	. 2 class (℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))
9	4, 8	wceq 1353	1 wff (℩𝑥 ∈ 𝐴 𝜑) = (℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))

This definition is referenced by:  riotaeqdv  5831  riotabidv  5832  riotaexg  5834  riotav  5835  riotauni  5836  nfriota1  5837  nfriotadxy  5838  cbvriota  5840  riotacl2  5843  riotabidva  5846  riota1  5848  riota2df  5850  snriota  5859  riotaund  5864  grpidvalg  12791  fn0g  12793  ismgmid  12795  oppr1g  13250  bdcriota  14605