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

Theorem riotav 5703
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 5698 . 2  |-  ( iota_ x  e.  _V  ph )  =  ( iota x
( x  e.  _V  /\ 
ph ) )
2 vex 2663 . . . 4  |-  x  e. 
_V
32biantrur 301 . . 3  |-  ( ph  <->  ( x  e.  _V  /\  ph ) )
43iotabii 5080 . 2  |-  ( iota
x ph )  =  ( iota x ( x  e.  _V  /\  ph ) )
51, 4eqtr4i 2141 1  |-  ( iota_ x  e.  _V  ph )  =  ( iota x ph )
Colors of variables: wff set class
Syntax hints:    /\ wa 103    = wceq 1316    e. wcel 1465   _Vcvv 2660   iotacio 5056   iota_crio 5697
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 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-rex 2399  df-v 2662  df-uni 3707  df-iota 5058  df-riota 5698
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator