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Theorem unabs 3516
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 3506 . 2  |-  ( A  i^i  B )  C_  A
2 ssequn2 3465 . 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 1649    u. cun 3263    i^i cin 3264    C_ wss 3265
This theorem is referenced by:  volun  19308
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-un 3270  df-in 3272  df-ss 3279
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