Theorem riotav 6516

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 6511	. 2 ⊢ (℩𝑥 ∈ V 𝜑) = (℩𝑥(𝑥 ∈ V ∧ 𝜑))
2		vex 3176	. . . 4 ⊢ 𝑥 ∈ V
3	2	biantrur 526	. . 3 ⊢ (𝜑 ↔ (𝑥 ∈ V ∧ 𝜑))
4	3	iotabii 5790	. 2 ⊢ (℩𝑥𝜑) = (℩𝑥(𝑥 ∈ V ∧ 𝜑))
5	1, 4	eqtr4i 2635	1 ⊢ (℩𝑥 ∈ V 𝜑) = (℩𝑥𝜑)

Syntax hints:   ∧ wa 383   = wceq 1475   ∈ wcel 1977  Vcvv 3173  ℩cio 5766  ℩crio 6510

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590

This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-rex 2902  df-v 3175  df-uni 4373  df-iota 5768  df-riota 6511

This theorem is referenced by: (None)