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Theorem riotav 6250
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 6245 . 2  |-  ( iota_ x  e.  _V  ph )  =  ( iota x
( x  e.  _V  /\ 
ph ) )
2 vex 3116 . . . 4  |-  x  e. 
_V
32biantrur 506 . . 3  |-  ( ph  <->  ( x  e.  _V  /\  ph ) )
43iotabii 5573 . 2  |-  ( iota
x ph )  =  ( iota x ( x  e.  _V  /\  ph ) )
51, 4eqtr4i 2499 1  |-  ( iota_ x  e.  _V  ph )  =  ( iota x ph )
Colors of variables: wff setvar class
Syntax hints:    /\ wa 369    = wceq 1379    e. wcel 1767   _Vcvv 3113   iotacio 5549   iota_crio 6244
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-rex 2820  df-v 3115  df-uni 4246  df-iota 5551  df-riota 6245
This theorem is referenced by: (None)
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