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Theorem riotav 5498
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 5493 . 2 (𝑥 ∈ V 𝜑) = (℩𝑥(𝑥 ∈ V ∧ 𝜑))
2 vex 2575 . . . 4 𝑥 ∈ V
32biantrur 291 . . 3 (𝜑 ↔ (𝑥 ∈ V ∧ 𝜑))
43iotabii 4914 . 2 (℩𝑥𝜑) = (℩𝑥(𝑥 ∈ V ∧ 𝜑))
51, 4eqtr4i 2077 1 (𝑥 ∈ V 𝜑) = (℩𝑥𝜑)
Colors of variables: wff set class
Syntax hints:  wa 101   = wceq 1257  wcel 1407  Vcvv 2572  cio 4890  crio 5492
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 638  ax-5 1350  ax-7 1351  ax-gen 1352  ax-ie1 1396  ax-ie2 1397  ax-8 1409  ax-10 1410  ax-11 1411  ax-i12 1412  ax-bndl 1413  ax-4 1414  ax-17 1433  ax-i9 1437  ax-ial 1441  ax-i5r 1442  ax-ext 2036
This theorem depends on definitions:  df-bi 114  df-tru 1260  df-nf 1364  df-sb 1660  df-clab 2041  df-cleq 2047  df-clel 2050  df-nfc 2181  df-rex 2327  df-v 2574  df-uni 3606  df-iota 4892  df-riota 5493
This theorem is referenced by: (None)
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