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Theorem riotav 6272
Description: An iota restricted to the universe is unrestricted. (Contributed by NM, 18-Sep-2011.)
Assertion
Ref Expression
riotav  |-  ( iota_ x  e.  _V  ph )  =  ( iota x ph )

Proof of Theorem riotav
StepHypRef Expression
1 df-riota 6267 . 2  |-  ( iota_ x  e.  _V  ph )  =  ( iota x
( x  e.  _V  /\ 
ph ) )
2 vex 3090 . . . 4  |-  x  e. 
_V
32biantrur 508 . . 3  |-  ( ph  <->  ( x  e.  _V  /\  ph ) )
43iotabii 5587 . 2  |-  ( iota
x ph )  =  ( iota x ( x  e.  _V  /\  ph ) )
51, 4eqtr4i 2461 1  |-  ( iota_ x  e.  _V  ph )  =  ( iota x ph )
Colors of variables: wff setvar class
Syntax hints:    /\ wa 370    = wceq 1437    e. wcel 1870   _Vcvv 3087   iotacio 5563   iota_crio 6266
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407
This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-rex 2788  df-v 3089  df-uni 4223  df-iota 5565  df-riota 6267
This theorem is referenced by: (None)
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