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Theorem riotav 6985
 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 6980 . 2 (𝑥 ∈ V 𝜑) = (℩𝑥(𝑥 ∈ V ∧ 𝜑))
2 vex 3439 . . . 4 𝑥 ∈ V
32biantrur 531 . . 3 (𝜑 ↔ (𝑥 ∈ V ∧ 𝜑))
43iotabii 6214 . 2 (℩𝑥𝜑) = (℩𝑥(𝑥 ∈ V ∧ 𝜑))
51, 4eqtr4i 2821 1 (𝑥 ∈ V 𝜑) = (℩𝑥𝜑)
 Colors of variables: wff setvar class Syntax hints:   ∧ wa 396   = wceq 1522   ∈ wcel 2080  Vcvv 3436  ℩cio 6190  ℩crio 6979 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1778  ax-4 1792  ax-5 1889  ax-6 1948  ax-7 1993  ax-8 2082  ax-9 2090  ax-ext 2768 This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1763  df-sb 2042  df-clab 2775  df-cleq 2787  df-clel 2862  df-rex 3110  df-v 3438  df-uni 4748  df-iota 6192  df-riota 6980 This theorem is referenced by: (None)
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