Definition df-riota 7324

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 6454. (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 7323	. 2 class (℩𝑥 ∈ 𝐴 𝜑)
5	2	cv 1541	. . . . 5 class 𝑥
6	5, 3	wcel 2114	. . . 4 wff 𝑥 ∈ 𝐴
7	6, 1	wa 395	. . 3 wff (𝑥 ∈ 𝐴 ∧ 𝜑)
8	7, 2	cio 6452	. 2 class (℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))
9	4, 8	wceq 1542	1 wff (℩𝑥 ∈ 𝐴 𝜑) = (℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))

This definition is referenced by:  riotaeqdv  7325  riotabidv  7326  riotaex  7328  riotav  7329  riotauni  7330  nfriota1  7331  nfriotadw  7332  cbvriotaw  7333  cbvriotavw  7334  nfriotad  7335  cbvriota  7337  csbriota  7339  riotacl2  7340  riotabidva  7343  riota1  7345  riota2df  7347  snriota  7357  riotaund  7363  riotarab  7366  ismgmid  18633  q1peqb  26121  adjval  31961  riotaeqbii  36380  cbvriotavw2  36418  cbvriotadavw  36452  cbvriotadavw2  36472