Users' Mathboxes Mathbox for Andrew Salmon < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  compeq Unicode version

Theorem compeq 27312
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 27311 . 2  |-  ( x  e.  ( _V  \  A )  <->  -.  x  e.  A )
21abbi2i 2500 1  |-  ( _V 
\  A )  =  { x  |  -.  x  e.  A }
Colors of variables: wff set class
Syntax hints:   -. wn 3    = wceq 1649    e. wcel 1717   {cab 2375   _Vcvv 2901    \ cdif 3262
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2370
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2376  df-cleq 2382  df-clel 2385  df-nfc 2514  df-v 2903  df-dif 3268
  Copyright terms: Public domain W3C validator