Theorem riotav 7376

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

Assertion

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

Proof of Theorem riotav

Step	Hyp	Ref	Expression
1		df-riota 7371	. 2 ⊢ (℩𝑥 ∈ V 𝜑) = (℩𝑥(𝑥 ∈ V ∧ 𝜑))
2		vex 3466	. . . 4 ⊢ 𝑥 ∈ V
3	2	biantrur 539	. . 3 ⊢ (𝜑 ↔ (𝑥 ∈ V ∧ 𝜑))
4	3	iotabii 6525	. 2 ⊢ (℩𝑥𝜑) = (℩𝑥(𝑥 ∈ V ∧ 𝜑))
5	1, 4	eqtr4i 2796	1 ⊢ (℩𝑥 ∈ V 𝜑) = (℩𝑥𝜑)

Syntax hints:   ∧ wa 400   = wceq 1568   ∈ wcel 2150  Vcvv 3462  ℩cio 6494  ℩crio 7370

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1823  ax-4 1837  ax-5 1938  ax-6 1995  ax-7 2036  ax-8 2152  ax-9 2160  ax-ext 2742

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1571  df-ex 1808  df-sb 2099  df-clab 2749  df-cleq 2762  df-clel 2845  df-v 3464  df-ss 3930  df-uni 4878  df-iota 6496  df-riota 7371

This theorem is referenced by: (None)