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Theorem rabab 2839
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 2586 . 2  |-  { x  e.  _V  |  ph }  =  { x  |  ( x  e.  _V  /\  ph ) }
2 vex 2825 . . . 4  |-  x  e. 
_V
32biantrur 492 . . 3  |-  ( ph  <->  ( x  e.  _V  /\  ph ) )
43abbii 2428 . 2  |-  { x  |  ph }  =  {
x  |  ( x  e.  _V  /\  ph ) }
51, 4eqtr4i 2339 1  |-  { x  e.  _V  |  ph }  =  { x  |  ph }
Colors of variables: wff set class
Syntax hints:    /\ wa 358    = wceq 1633    e. wcel 1701   {cab 2302   {crab 2581   _Vcvv 2822
This theorem is referenced by:  notab  3472  intmin2  3926  euen1  6974  cardf2  7621  hsmex2  8104  ballotlemfmpn  23926  imageval  24854  rmxyelqirr  26143
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1537  ax-5 1548  ax-17 1607  ax-9 1645  ax-8 1666  ax-6 1720  ax-7 1725  ax-11 1732  ax-12 1897  ax-ext 2297
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1533  df-nf 1536  df-sb 1640  df-clab 2303  df-cleq 2309  df-clel 2312  df-rab 2586  df-v 2824
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