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Theorem unabs 3563
Description: Absorption law for union. (Contributed by NM, 16-Apr-2006.)
Assertion
Ref Expression
unabs  |-  ( A  u.  ( A  i^i  B ) )  =  A

Proof of Theorem unabs
StepHypRef Expression
1 inss1 3553 . 2  |-  ( A  i^i  B )  C_  A
2 ssequn2 3512 . 2  |-  ( ( A  i^i  B ) 
C_  A  <->  ( A  u.  ( A  i^i  B
) )  =  A )
31, 2mpbi 200 1  |-  ( A  u.  ( A  i^i  B ) )  =  A
Colors of variables: wff set class
Syntax hints:    = wceq 1652    u. cun 3310    i^i cin 3311    C_ wss 3312
This theorem is referenced by:  volun  19431
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-un 3317  df-in 3319  df-ss 3326
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