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Theorem rabab 2758
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 2464 . 2  |-  { x  e.  _V  |  ph }  =  { x  |  ( x  e.  _V  /\  ph ) }
2 vex 2740 . . . 4  |-  x  e. 
_V
32biantrur 303 . . 3  |-  ( ph  <->  ( x  e.  _V  /\  ph ) )
43abbii 2293 . 2  |-  { x  |  ph }  =  {
x  |  ( x  e.  _V  /\  ph ) }
51, 4eqtr4i 2201 1  |-  { x  e.  _V  |  ph }  =  { x  |  ph }
Colors of variables: wff set class
Syntax hints:    /\ wa 104    = wceq 1353    e. wcel 2148   {cab 2163   {crab 2459   _Vcvv 2737
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-11 1506  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-rab 2464  df-v 2739
This theorem is referenced by:  notab  3405  intmin2  3868  euen1  6795  bj-omind  14308
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