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Theorem riotav 7119
 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
StepHypRef Expression
1 df-riota 7114 . 2 (𝑥 ∈ V 𝜑) = (℩𝑥(𝑥 ∈ V ∧ 𝜑))
2 vex 3413 . . . 4 𝑥 ∈ V
32biantrur 534 . . 3 (𝜑 ↔ (𝑥 ∈ V ∧ 𝜑))
43iotabii 6325 . 2 (℩𝑥𝜑) = (℩𝑥(𝑥 ∈ V ∧ 𝜑))
51, 4eqtr4i 2784 1 (𝑥 ∈ V 𝜑) = (℩𝑥𝜑)
 Colors of variables: wff setvar class Syntax hints:   ∧ wa 399   = wceq 1538   ∈ wcel 2111  Vcvv 3409  ℩cio 6297  ℩crio 7113 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2729 This theorem depends on definitions:  df-bi 210  df-an 400  df-tru 1541  df-ex 1782  df-sb 2070  df-clab 2736  df-cleq 2750  df-clel 2830  df-v 3411  df-in 3867  df-ss 3877  df-uni 4802  df-iota 6299  df-riota 7114 This theorem is referenced by: (None)
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