This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem riotaex

Description: Restricted iota is a set. (Contributed by NM, 15-Sep-2011)

		Ref	Expression
	Assertion	riotaex	⊢ ( ℩ 𝑥 ∈ 𝐴 𝜓 ) ∈ V

Step	Hyp	Ref	Expression
1		df-riota	⊢ ( ℩ 𝑥 ∈ 𝐴 𝜓 ) = ( ℩ 𝑥 ( 𝑥 ∈ 𝐴 ∧ 𝜓 ) )
2		iotaex	⊢ ( ℩ 𝑥 ( 𝑥 ∈ 𝐴 ∧ 𝜓 ) ) ∈ V
3	1 2	eqeltri	⊢ ( ℩ 𝑥 ∈ 𝐴 𝜓 ) ∈ V