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Metamath Proof Explorer

Definition df-riota

Description: Define restricted description binder. In case there is no unique x such that ( x e. A /\ ph ) holds, it evaluates to the empty set. See also comments for df-iota . (Contributed by NM, 15-Sep-2011) (Revised by Mario Carneiro, 15-Oct-2016) (Revised by NM, 2-Sep-2018)

		Ref	Expression
	Assertion	df-riota	$⊢ (ι x \in A \| φ) = (ι x \| (x \in A \land φ))$

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		vx	$setvar x$
1		cA	$class A$
2		wph	$wff φ$
3	2 0 1	crio	$class (ι x \in A \| φ)$
4	0	cv	$setvar x$
5	4 1	wcel	$wff x \in A$
6	5 2	wa	$wff (x \in A \land φ)$
7	6 0	cio	$class (ι x \| (x \in A \land φ))$
8	3 7	wceq	$wff (ι x \in A \| φ) = (ι x \| (x \in A \land φ))$