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Theorem riotav 7365
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 7360 . 2 (𝑥 ∈ V 𝜑) = (℩𝑥(𝑥 ∈ V ∧ 𝜑))
2 vex 3472 . . . 4 𝑥 ∈ V
32biantrur 530 . . 3 (𝜑 ↔ (𝑥 ∈ V ∧ 𝜑))
43iotabii 6521 . 2 (℩𝑥𝜑) = (℩𝑥(𝑥 ∈ V ∧ 𝜑))
51, 4eqtr4i 2757 1 (𝑥 ∈ V 𝜑) = (℩𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wa 395   = wceq 1533  wcel 2098  Vcvv 3468  cio 6486  crio 7359
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2697
This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2704  df-cleq 2718  df-clel 2804  df-v 3470  df-in 3950  df-ss 3960  df-uni 4903  df-iota 6488  df-riota 7360
This theorem is referenced by: (None)
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