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Theorem compeq 27609
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 27608 . 2  |-  ( x  e.  ( _V  \  A )  <->  -.  x  e.  A )
21abbi2i 2546 1  |-  ( _V 
\  A )  =  { x  |  -.  x  e.  A }
Colors of variables: wff set class
Syntax hints:   -. wn 3    = wceq 1652    e. wcel 1725   {cab 2421   _Vcvv 2948    \ cdif 3309
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-or 360  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-nfc 2560  df-v 2950  df-dif 3315
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