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Theorem rabab 3124
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 2816 . 2  |-  { x  e.  _V  |  ph }  =  { x  |  ( x  e.  _V  /\  ph ) }
2 vex 3109 . . . 4  |-  x  e. 
_V
32biantrur 506 . . 3  |-  ( ph  <->  ( x  e.  _V  /\  ph ) )
43abbii 2594 . 2  |-  { x  |  ph }  =  {
x  |  ( x  e.  _V  /\  ph ) }
51, 4eqtr4i 2492 1  |-  { x  e.  _V  |  ph }  =  { x  |  ph }
Colors of variables: wff setvar class
Syntax hints:    /\ wa 369    = wceq 1374    e. wcel 1762   {cab 2445   {crab 2811   _Vcvv 3106
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-10 1781  ax-11 1786  ax-12 1798  ax-13 1961  ax-ext 2438
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1377  df-ex 1592  df-nf 1595  df-sb 1707  df-clab 2446  df-cleq 2452  df-clel 2455  df-rab 2816  df-v 3108
This theorem is referenced by:  notab  3761  intmin2  4302  euen1  7575  cardf2  8313  hsmex2  8802  imageval  29143  rmxyelqirr  30437
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