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Theorem rabab 3076
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 2762 . 2  |-  { x  e.  _V  |  ph }  =  { x  |  ( x  e.  _V  /\  ph ) }
2 vex 3061 . . . 4  |-  x  e. 
_V
32biantrur 504 . . 3  |-  ( ph  <->  ( x  e.  _V  /\  ph ) )
43abbii 2536 . 2  |-  { x  |  ph }  =  {
x  |  ( x  e.  _V  /\  ph ) }
51, 4eqtr4i 2434 1  |-  { x  e.  _V  |  ph }  =  { x  |  ph }
Colors of variables: wff setvar class
Syntax hints:    /\ wa 367    = wceq 1405    e. wcel 1842   {cab 2387   {crab 2757   _Vcvv 3058
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380
This theorem depends on definitions:  df-bi 185  df-an 369  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-rab 2762  df-v 3060
This theorem is referenced by:  notab  3719  intmin2  4254  euen1  7622  cardf2  8355  hsmex2  8844  imageval  30255  rmxyelqirr  35187  dfrcl2  35633
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