Theorem riotav

Description: An iota restricted to the universe is unrestricted. (Contributed by NM, 18-Sep-2011)

	Ref	Expression
Assertion	riotav	⊢ ( ℩ 𝑥 ∈ V 𝜑 ) = ( ℩ 𝑥 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		df-riota	⊢ ( ℩ 𝑥 ∈ V 𝜑 ) = ( ℩ 𝑥 ( 𝑥 ∈ V ∧ 𝜑 ) )
2		vex	⊢ 𝑥 ∈ V
3	2	biantrur	⊢ ( 𝜑 ↔ ( 𝑥 ∈ V ∧ 𝜑 ) )
4	3	iotabii	⊢ ( ℩ 𝑥 𝜑 ) = ( ℩ 𝑥 ( 𝑥 ∈ V ∧ 𝜑 ) )
5	1 4	eqtr4i	⊢ ( ℩ 𝑥 ∈ V 𝜑 ) = ( ℩ 𝑥 𝜑 )