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Theorem compeq 27641
Description: Equality between two ways of saying "the complement of 
A." (Contributed by Andrew Salmon, 15-Jul-2011.)
Assertion
Ref Expression
compeq  |-  ( _V 
\  A )  =  { x  |  -.  x  e.  A }
Distinct variable group:    x, A

Proof of Theorem compeq
StepHypRef Expression
1 compel 27640 . 2  |-  ( x  e.  ( _V  \  A )  <->  -.  x  e.  A )
21abbi2i 2394 1  |-  ( _V 
\  A )  =  { x  |  -.  x  e.  A }
Colors of variables: wff set class
Syntax hints:   -. wn 3    = wceq 1623    e. wcel 1684   {cab 2269   _Vcvv 2788    \ cdif 3149
This theorem is referenced by:  compneOLD  27643
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-dif 3155
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