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Theorem rabab 2702
Description: A class abstraction restricted to the universe is unrestricted. (Contributed by NM, 27-Dec-2004.) (Proof shortened by Andrew Salmon, 8-Jun-2011.)
Assertion
Ref Expression
rabab  |-  { x  e.  _V  |  ph }  =  { x  |  ph }

Proof of Theorem rabab
StepHypRef Expression
1 df-rab 2423 . 2  |-  { x  e.  _V  |  ph }  =  { x  |  ( x  e.  _V  /\  ph ) }
2 vex 2684 . . . 4  |-  x  e. 
_V
32biantrur 301 . . 3  |-  ( ph  <->  ( x  e.  _V  /\  ph ) )
43abbii 2253 . 2  |-  { x  |  ph }  =  {
x  |  ( x  e.  _V  /\  ph ) }
51, 4eqtr4i 2161 1  |-  { x  e.  _V  |  ph }  =  { x  |  ph }
Colors of variables: wff set class
Syntax hints:    /\ wa 103    = wceq 1331    e. wcel 1480   {cab 2123   {crab 2418   _Vcvv 2681
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-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-11 1484  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-rab 2423  df-v 2683
This theorem is referenced by:  notab  3341  intmin2  3792  euen1  6689  bj-omind  13121
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