Theorem riotacl

Description: Closure of restricted iota. (Contributed by NM, 21-Aug-2011)

	Ref	Expression
Assertion	riotacl	$$⊢\exists !x\in A\phi \to \left(\iota x\in A|\phi \right)\in A$$

Proof

Step	Hyp	Ref	Expression
1		ssrab2	$$⊢\left\{x\in A|\phi \right\}\subseteq A$$
2		riotacl2	$$⊢\exists !x\in A\phi \to \left(\iota x\in A|\phi \right)\in \left\{x\in A|\phi \right\}$$
3	1 2	sseldi	$$⊢\exists !x\in A\phi \to \left(\iota x\in A|\phi \right)\in A$$