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Theorem riotav 6570
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 6565 . 2 (𝑥 ∈ V 𝜑) = (℩𝑥(𝑥 ∈ V ∧ 𝜑))
2 vex 3189 . . . 4 𝑥 ∈ V
32biantrur 527 . . 3 (𝜑 ↔ (𝑥 ∈ V ∧ 𝜑))
43iotabii 5832 . 2 (℩𝑥𝜑) = (℩𝑥(𝑥 ∈ V ∧ 𝜑))
51, 4eqtr4i 2646 1 (𝑥 ∈ V 𝜑) = (℩𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wa 384   = wceq 1480  wcel 1987  Vcvv 3186  cio 5808  crio 6564
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-rex 2913  df-v 3188  df-uni 4403  df-iota 5810  df-riota 6565
This theorem is referenced by: (None)
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