Theorem riotav 6616

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 6611	. 2 ⊢ (℩𝑥 ∈ V 𝜑) = (℩𝑥(𝑥 ∈ V ∧ 𝜑))
2		vex 3203	. . . 4 ⊢ 𝑥 ∈ V
3	2	biantrur 527	. . 3 ⊢ (𝜑 ↔ (𝑥 ∈ V ∧ 𝜑))
4	3	iotabii 5873	. 2 ⊢ (℩𝑥𝜑) = (℩𝑥(𝑥 ∈ V ∧ 𝜑))
5	1, 4	eqtr4i 2647	1 ⊢ (℩𝑥 ∈ V 𝜑) = (℩𝑥𝜑)

Syntax hints:   ∧ wa 384   = wceq 1483   ∈ wcel 1990  Vcvv 3200  ℩cio 5849  ℩crio 6610

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-rex 2918  df-v 3202  df-uni 4437  df-iota 5851  df-riota 6611

This theorem is referenced by: (None)