ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  riotav Unicode version

Theorem riotav 5742
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 5737 . 2  |-  ( iota_ x  e.  _V  ph )  =  ( iota x
( x  e.  _V  /\ 
ph ) )
2 vex 2692 . . . 4  |-  x  e. 
_V
32biantrur 301 . . 3  |-  ( ph  <->  ( x  e.  _V  /\  ph ) )
43iotabii 5117 . 2  |-  ( iota
x ph )  =  ( iota x ( x  e.  _V  /\  ph ) )
51, 4eqtr4i 2164 1  |-  ( iota_ x  e.  _V  ph )  =  ( iota x ph )
Colors of variables: wff set class
Syntax hints:    /\ wa 103    = wceq 1332    e. wcel 1481   _Vcvv 2689   iotacio 5093   iota_crio 5736
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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122
This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-rex 2423  df-v 2691  df-uni 3744  df-iota 5095  df-riota 5737
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator