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Theorem rabab 2965
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 2706 . 2  |-  { x  e.  _V  |  ph }  =  { x  |  ( x  e.  _V  /\  ph ) }
2 vex 2951 . . . 4  |-  x  e. 
_V
32biantrur 493 . . 3  |-  ( ph  <->  ( x  e.  _V  /\  ph ) )
43abbii 2547 . 2  |-  { x  |  ph }  =  {
x  |  ( x  e.  _V  /\  ph ) }
51, 4eqtr4i 2458 1  |-  { x  e.  _V  |  ph }  =  { x  |  ph }
Colors of variables: wff set class
Syntax hints:    /\ wa 359    = wceq 1652    e. wcel 1725   {cab 2421   {crab 2701   _Vcvv 2948
This theorem is referenced by:  notab  3603  intmin2  4069  euen1  7169  cardf2  7822  hsmex2  8305  imageval  25767  rmxyelqirr  26964
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-rab 2706  df-v 2950
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