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Theorem unabs 3735
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 3714 . 2  |-  ( A  i^i  B )  C_  A
2 ssequn2 3673 . 2  |-  ( ( A  i^i  B ) 
C_  A  <->  ( A  u.  ( A  i^i  B
) )  =  A )
31, 2mpbi 208 1  |-  ( A  u.  ( A  i^i  B ) )  =  A
Colors of variables: wff setvar class
Syntax hints:    = wceq 1395    u. cun 3469    i^i cin 3470    C_ wss 3471
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-un 3476  df-in 3478  df-ss 3485
This theorem is referenced by:  volun  22080
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