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Theorem unabs 3167
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 3157 . 2  |-  ( A  i^i  B )  C_  A
2 ssequn2 3116 . 2  |-  ( ( A  i^i  B ) 
C_  A  <->  ( A  u.  ( A  i^i  B
) )  =  A )
31, 2mpbi 133 1  |-  ( A  u.  ( A  i^i  B ) )  =  A
Colors of variables: wff set class
Syntax hints:    = wceq 1243    u. cun 2915    i^i cin 2916    C_ wss 2917
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-in 2924  df-ss 2931
This theorem is referenced by: (None)
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