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Theorem riotav 5701
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 5696 . 2 (𝑥 ∈ V 𝜑) = (℩𝑥(𝑥 ∈ V ∧ 𝜑))
2 vex 2661 . . . 4 𝑥 ∈ V
32biantrur 299 . . 3 (𝜑 ↔ (𝑥 ∈ V ∧ 𝜑))
43iotabii 5078 . 2 (℩𝑥𝜑) = (℩𝑥(𝑥 ∈ V ∧ 𝜑))
51, 4eqtr4i 2139 1 (𝑥 ∈ V 𝜑) = (℩𝑥𝜑)
Colors of variables: wff set class
Syntax hints:  wa 103   = wceq 1314  wcel 1463  Vcvv 2658  cio 5054  crio 5695
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-rex 2397  df-v 2660  df-uni 3705  df-iota 5056  df-riota 5696
This theorem is referenced by: (None)
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